Optimal timing for financial and economic decisions under adverse and stressful conditions

Lead Research Organisation: Queen Mary, University of London
Department Name: Sch of Mathematical Sciences

Abstract

Stochastic control theory can be viewed as the mathematical theory of controlling a stochastic process, which models the dynamics of a physical phenomenon, in view of optimising a certain criterion. It has found applications in finance, economics, physics, engineering and biology, which makes any new development in the theory quite important. This proposal will focus on two novel types of problems from the subclasses of optimal stopping theory, where control takes the form of an one-off stopping, and of the theory of stochastic control games. This research will address the timing of decision making by different market perspectives, namely by individuals, businesses, financial institutions and governmental bodies, in the setting of adverse and stressful conditions that have not been mathematically treated before. It will therefore also extend the application span of this well-established theory in the world of finance and economics, as well as attempt to bridge it with social sciences, such as behavioural economics, government policy and macroeconomics. The main objective is that the results of this work will give a review of different market participants' reactions and the impact of their decisions' on the success of their strategies, but also on the general public.

In particular, the optimal decision timing when the decision makers have time-restrictions, due to their intolerance of adverse market movements or their impatience when their assets do not perform well for a significant amount of time, will be mathematically formulated and solved as two innovative time-constrained optimal stopping problems. Different optimisation criteria will be considered dealing with a diverse spectrum of financial settings, e.g. intolerance to credit events, closure of trading accounts or redundancy of an asset manager when underperforming, need for an early liquidation, compulsory exit from a non-sustainable project or voluntary abandonment of a low-performing one. In addition, different stochastic processes will be used to model the evolution of asset values, e.g. (continuous) diffusion models, or Levy models with jumps.

Finally, this proposal will study a game of controlling the government's debt-to-GDP ratio between the government itself and its bond holders, whose actions affect the level (singular control) and its dynamics (classical control), respectively. The government aims to control its debt-to-GDP ratio in view of minimising derived costs, while it also needs to consider the adverse behaviour of the holders of government bonds, who trade them to optimise their individual criterion. Mathematically, this translates to a non-zero-sum game of classical-singular stochastic control, a novel setting in the existing literature. This governmental task is important both for the government itself, which wants to prevent the direct multiple unpleasant consequences of a high debt-to-GDP ratio, and for the country's citizens, whose lives are indirectly affected in an economically negative way. In modern finance, this work may also find applications in controlling a company's share price, portfolio's value, or company's debt-to-equity ratio, only to name a few.

Planned Impact

The UK and London in particular is one of the world's largest financial centres. As such, the academic community bears the responsibility to support the nation's strategic position with groundbreaking financial and mathematical research. This proposal aims to contribute to the vision through research on time-constrained optimal stopping and game-type stochastic control theory, which focus on the optimal timing of decision making as a response to adverse market changes. With publications in high-impact journals and actively making this work accessible though conference talks and seminars, this proposal will help advance research in this field, setting the infrastructure for cross-disciplinary collaboration between financial mathematics, behavioural economics and government policy studies.

Results will also impact practitioners (individuals, businesses and financial institutions), which are either completely intolerant to specific adverse market movements, or impatient when their assets are underperforming for a significant amount of time. The tools provided will help optimise their decision making processes, as well as support the regulatory decisions on acceptable market drops by the Commodity Futures Trading Commission and Commodity Trading Advisors. From a government perspective, results will contribute to the methodology of quantifying the effects of controlling the government's debt-to-GDP ratio, thus help shape policies regarding its optimal control against adverse trading of its bonds. The governmental, societal and economic importance of controlling this ratio is paramount.

Publications

10 25 50
 
Description All research objectives of the grant proposal have been met. The proposal was split into two phases.

The first phase is devoted to the development of quantitative ways to optimally make investment decisions under periods of adverse market conditions and stress (of different types). This can be useful for members of the public or organisations which operate on behalf of the public amongst others. We can take as an example a pension fund whose assets (e.g. bonds, property etc.) have lower than anticipated value for a significant amount of time. Amongst many other reasons, this could be caused by an economic crisis, or simply an unfortunate investment. The results of the completed research supported by this grant, would help minimise the losses incurred to the fund and subsequently to the pensioner, by providing an optimal exit time. In this particular example, we see a social and economic impact. Typically, such decisions are made based on qualitative criteria and can now be improved with the use of a quantitative, more accurate approach given a set of assumptions. Findings of this research have been the result of cross-disciplinary pollination of behavioural economics and financial mathematics, therefore creating a bridge for further work.

The second phase is devoted to the development of quantitative tools, for governmental bodies, policy makers and other government research teams, working in relation to the optimal management of the country's debt-to-GDP ratio - a fundamental market indicator for the country - in an economy that can adversely change regimes at future random times. The objective would be to optimally use fiscal policies and make investment decisions under periods of adverse market conditions. We can take as an example a government which is faced with a high debt-to-GDP ratio level, which has negative economic implications for the country. Amongst many other reasons, this could be caused by an economic crisis, or simply an unfortunate investment / policy decision. The results of the completed research supported by this grant, could help minimise the losses incurred by the government and subsequently by the taxpayer, by providing an optimal intervention strategy. Namely, the strategy that optimally balances the benefits from improving the county's economic position (via decreasing the level of the ratio) against the taxpayers' burden by the employment of austerity policies (used in order to achieve the decrease of the ratio). In this particular example, the social and economic impact relates to best managing the economic losses from high debt-to-GDP ratio and the implications this may have on taxpayers and their future financial security. Typically, such decisions are made based on qualitative criteria and can now be improved with the use of a quantitative, more accurate approach given a set of assumptions. Findings of this research have been the result of cross-disciplinary pollination between political economics and financial mathematics, therefore creating a bridge for further work.
Exploitation Route Findings from the first part of this research can be used by academics from both behavioural economics and financial mathematics fields to progress cross-disciplinary research in this space. Longer term it can also be used by investors, such as members of the public, organisations that represent the pubic, business and many others, with the objective to optimally make investment decisions under periods of adverse market conditions and stress. The model provided is sufficiently generic and can be adjusted to meet various scenarios depending on the circumstances and user's needs. Given this research has only recently been completed, I will focus moving forward on making this accessible to the relevant audiences through the channels described in the grant application.

Findings from the second part of this research can be used by academics from macroeconomics, governmental policy and mathematical economics fields to progress¬ cross-disciplinary research in this space. Longer term it can also be used by governmental bodies, policy makers and other government research teams, working in relation to the optimal management of the country's debt-to-GDP ratio and other key macroeconomic indicators that affect the country's economic standing. The objective would be to optimally use fiscal policies and make investment decisions under periods of adverse market conditions. The model provided can be adjusted to meet various scenarios depending on the circumstances and the country's economic state. Even though this research has only recently been completed, the research findings have been presented to the Bank of England and HM Treasury. I will focus moving forward on making this more accessible to the relevant audiences through the channels described in the grant application.
Sectors Financial Services, and Management Consultancy,Government, Democracy and Justice,Other

 
Description Bielefeld University - Optimal timing for governmental debt-to-GDP ratio control 
Organisation Bielefeld University
Country Germany 
Sector Academic/University 
PI Contribution I have contributed to this work by (a) conceiving and structuring the research topic, (b) my expertise in zero-sum games, regime-switching problems, optimal stopping (c) providing the appropriate facilities and travel funds for the research to be carried out
Collaborator Contribution My collaborator Giorgio Ferrari has contributed with (a) his expertise in stochastic control theory (b) his experience in the application of such theory in economics and finance. He is also based at Bielefeld University and affiliated with the Center for Mathematical Economics (IMW), one of the leading European research centres in the field of (mathematical) economic theory; a hub for innovative, interdisciplinary research in mathematical and social sciences. He is therefore able to (c) also contribute with his network of economists who regularly advise us on applications and impact of our research on governmental policy.
Impact The research is cross disciplinary and links Mathematics and Macroeconomics, in particular, Probability Theory and Government debt policy. This collaboration has provided a quantitative approach to describing and studying the actions of a government that wishes to manage the country's debt, under macroeconomic risks that can adversely affect the country's economic planning, which have been analysed by political economists. As a result, this work has paved a route of connection between the two disciplines.
Start Year 2017
 
Description Columbia University - Optimal timing for selling an asset amid anxiety about price jumps and decreasing asset prices 
Organisation Columbia University
Country United States 
Sector Academic/University 
PI Contribution This collaboration relates to the research topic: "Optimal timing for selling an asset amid anxiety about price jumps and decreasing asset prices". I have contributed with (a) conceiving the research topic, (b) my expertise in the area of optimal stopping and multi-dimensional random processes, which are fundamental to the research, and also (c) in providing our collaboration team with the appropriate facilities and travel funds to carry out the research.
Collaborator Contribution My collaborator at Columbia University (Hongzhong Zhang), being the author of the recently published book "Stochastic Drawdowns", has contributed his expertise in drawdown risks, which are fundamental for this research, and his expertise in applications of applied probability for finance, engineering and insurance. This has been important for aligning our research to industry needs. He also brings the appropriate connections with behavioural scientists at Columbia University that have advised us on the cross disciplinary aspects of our research.
Impact This is the second phase of the research undertaken by the same authors in a paper titled "Beating the Omega Clock: An optimal stopping problem with random time-horizon under spectrally negative Levy processes". That initial work is already published by the journal: Annals of Applied Probability with DOI:10.1214/17-AAP1322. In particular, the research builds on the mathematics of the aforementioned completed project in order to study a much more complex problem, which enhances the cross disciplinary links between Mathematics and Social Sciences. More specifically this links Probability Theory and Behavioural Economics. This collaboration aims at providing a quantitative approach to describing and studying some additional interesting findings on loss aversion, especially under adverse and stressful market conditions, which have been found by behavioural economists from a psychological viewpoint. In particular, it makes a clear distinction between an individual's risk aversion and stress/impatience. Certain loss-preventing actions, that could not be captured by traditional risk aversion theory, are now quantitatively and qualitatively explained via our model for anxiety/impatience. As a result, this research aims at strengthening the connections between the two disciplines, which was paved in the first phase.
Start Year 2018
 
Description Columbia University - Optimal timing for selling an asset amid anxiety about price jumps and low asset prices. 
Organisation Columbia University
Country United States 
Sector Academic/University 
PI Contribution This collaboration relates to the research topic: "Optimal timing for selling an asset amid anxiety about price jumps and low asset prices". I have contributed with (a) conceiving the research topic, (b) my expertise in the area of Optimal Stopping which is fundamental to the research and also (c) in providing our collaboration team with the appropriate facilities to carry out the research.
Collaborator Contribution My collaborator at Columbia University (Hongzhong Zhang), has contributed with his expertise in applications of applied probability for finance, engineering and insurance. This is fundamental to well aligning our research to industry needs. He also brings the appropriate connections with behavioral scientists at Columbia University that have advised us on the cross disciplinary aspects of our research.
Impact This is the first phase of a research project that has been completed with a paper titled "Beating the Omega Clock: An optimal stopping problem with random time-horizon under spectrally negative Levy processes". This is already published by the journal: Annals of Applied Probability with DOI:10.1214/17-AAP1322. The research is cross disciplinary and links Mathematics and Social Sciences, in particular, Probability Theory and Behavioural Economics. This collaboration has provided a quantitative approach to describing and studying some interesting findings on loss aversion, especially under adverse and stressful market conditions, which have been found by behavioural economists from a psychological viewpoint. As a result, this work has paved a route of connection between the two disciplines.
Start Year 2017
 
Description LSE & University of Michigan - Stopping a SDE with generalised drift 
Organisation London School of Economics and Political Science (University of London)
Country United Kingdom 
Sector Academic/University 
PI Contribution This collaboration relates to the research topic: "Optimal timing for decision making under psychological market particularities". I have contributed with (a) my expertise in the area of Optimal Stopping which is the main theory for decision timing and therefore the fundamental pillar for carrying out the research and also (b) in providing our collaboration team with the appropriate funds to carry out the research and present it in global fora.
Collaborator Contribution My collaborators at the LSE (London School of Economics) (Mihail Zervos) and University of Michigan (Thomas Bernhardt) have contributed with their expertise on Variational Inequalities and Measure Theory which were fundamental components of the analysis. Prof M. Zervos (Head of Financial Mathematics group of the LSE) has also brought the appropriate connections with finance experts and economists at the LSE that have advised us on the cross disciplinary aspects of our research.
Impact Beyond its contributions to the theoretical optimal stopping theory, this project provides a mathematical framework describing the optimal timing of investment decisions when the financial market exhibits certain (psychological) particularities. In particular, it provides a technique for optimal decision making, when (A) dealing with phenomena of bounces and sinks of financial firms in distress and (B) dealing with asset prices or economic indicators that: (i) either exhibit support and resistance levels - buying/selling interest is sufficiently strong to overcome selling/buying pressure; (ii) or are affected by other psychological features that lead to directional predictability of their future value. This project therefore strengthens the long-standing links of mathematics with finance and economics, by providing the aforementioned new mathematical theory to support their decision making processes.
Start Year 2017
 
Description LSE & University of Michigan - Stopping a SDE with generalised drift 
Organisation University of Michigan
Country United States 
Sector Academic/University 
PI Contribution This collaboration relates to the research topic: "Optimal timing for decision making under psychological market particularities". I have contributed with (a) my expertise in the area of Optimal Stopping which is the main theory for decision timing and therefore the fundamental pillar for carrying out the research and also (b) in providing our collaboration team with the appropriate funds to carry out the research and present it in global fora.
Collaborator Contribution My collaborators at the LSE (London School of Economics) (Mihail Zervos) and University of Michigan (Thomas Bernhardt) have contributed with their expertise on Variational Inequalities and Measure Theory which were fundamental components of the analysis. Prof M. Zervos (Head of Financial Mathematics group of the LSE) has also brought the appropriate connections with finance experts and economists at the LSE that have advised us on the cross disciplinary aspects of our research.
Impact Beyond its contributions to the theoretical optimal stopping theory, this project provides a mathematical framework describing the optimal timing of investment decisions when the financial market exhibits certain (psychological) particularities. In particular, it provides a technique for optimal decision making, when (A) dealing with phenomena of bounces and sinks of financial firms in distress and (B) dealing with asset prices or economic indicators that: (i) either exhibit support and resistance levels - buying/selling interest is sufficiently strong to overcome selling/buying pressure; (ii) or are affected by other psychological features that lead to directional predictability of their future value. This project therefore strengthens the long-standing links of mathematics with finance and economics, by providing the aforementioned new mathematical theory to support their decision making processes.
Start Year 2017
 
Description Advisory working sessions with Bank of England 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact 4 formal advisory sessions with Bank of England experts, led by Gerardo Ferrara (Economist FMI Risk, Research & CCP Policy). The purpose was to leverage their technical and macroeconomic expertise in order to ensure feasibility and relevance of research assumptions. These sessions helped ensure that the problem formulation and model produced through this research are aligned with economic needs and real life situations. They were also helpful in framing the impact of the research. The aforementioned input was gratefully acknowledged also in the research paper entitled "Optimal control of debt-to-GDP ratio in an N-state regime switching economy".
Year(s) Of Engagement Activity 2018,2019
URL https://arxiv.org/pdf/1808.01499.pdf
 
Description Advisory working sessions with Lloyds Banking Group, Credit Suisse and Citi Bank 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact 6 formal advisory sessions with finance industry experts were held with Lloyds banking group, led by Harry Rizopoulos (FX Options trader), with Credit Suisse, led by Paris Hadjiantonis (Equity Research Analyst) and with Citi bank, led by Filippo Riccardi (Equity derivatives trader). The purpose was to leverage the group's technical and industry expertise in order to ensure feasibility and relevance of research assumptions. These sessions helped ensure that the problem formulations and models produced through this research are aligned with market needs and real life situations. They were also helpful in framing the impact of the research.
Year(s) Of Engagement Activity 2017,2018