# Equilibrium asset pricing with power utility

Lead Research Organisation:
University of Warwick

Department Name: Statistics

### Abstract

The goal of this research project is to characterise the equilibrium dynamics of assets arising in different types of equilibria: with endogenous returns, endogenous volatility, and endogenous interest rates, respectively. The first goal is to study the frictionless case in both complete and incomplete markets and compare this to the extant literature. Whereas the case of exponential utility is by now well understood, see e.g. [2], [3], [6], the case of power utility is largely open. The next goal is then to extend the results to transaction costs. Here the case of mean-variance utilities is well understood, see [1] and [4], and partial results exist for exponential utilities [5].

Mathematically, the problem is linked to systems of forward-backward stochastic differential equations. Unlike in the case of exponential utilities, the forward and the backward equations are coupled in the case of power utility. So, an important problem is to prove well-posedness, existence and uniqueness of those FBSDE systems.

References:

[1] B. Bouchard, M. Fukasawa, M. Herdegen, and J. Muhle-Karbe. Equilibrium returns with transaction costs. Finance and Stochastics, 22:569-601, 2018.

[2] Escauriaza, Xing and Schwarz: Radner equilibrium and systems of quadratic BSDEs with discontinuous generators, 2021.

[3] P. Guasoni and M. H. Weber. Incomplete-market equilibrium with unhedgeable fundamentals and heterogenous agents. Michael J. Brennan Irish Finance Working Paper Series, 2022.

[4] M. Herdegen, J. Muhle-Karbe and D. Possamai: Equilibrium asset pricing with transaction costs, Finance and Stochastics, 25:231-275, 2021.

[5] M. Herdegen and J. Muhle-Karbe: Stability of Radner equilibria with respect to small frictions, Finance and Stochastics, 22:443-502, 2018.

[6] C. Kardaras, H. Xing, and G. Zitkovic. Incomplete stochastic equilibria with exponential utilities close to pareto optimality. Stochastic Analysis, Filterting and Stochastic Optimisation, pages 267-292, 2022.

Mathematically, the problem is linked to systems of forward-backward stochastic differential equations. Unlike in the case of exponential utilities, the forward and the backward equations are coupled in the case of power utility. So, an important problem is to prove well-posedness, existence and uniqueness of those FBSDE systems.

References:

[1] B. Bouchard, M. Fukasawa, M. Herdegen, and J. Muhle-Karbe. Equilibrium returns with transaction costs. Finance and Stochastics, 22:569-601, 2018.

[2] Escauriaza, Xing and Schwarz: Radner equilibrium and systems of quadratic BSDEs with discontinuous generators, 2021.

[3] P. Guasoni and M. H. Weber. Incomplete-market equilibrium with unhedgeable fundamentals and heterogenous agents. Michael J. Brennan Irish Finance Working Paper Series, 2022.

[4] M. Herdegen, J. Muhle-Karbe and D. Possamai: Equilibrium asset pricing with transaction costs, Finance and Stochastics, 25:231-275, 2021.

[5] M. Herdegen and J. Muhle-Karbe: Stability of Radner equilibria with respect to small frictions, Finance and Stochastics, 22:443-502, 2018.

[6] C. Kardaras, H. Xing, and G. Zitkovic. Incomplete stochastic equilibria with exponential utilities close to pareto optimality. Stochastic Analysis, Filterting and Stochastic Optimisation, pages 267-292, 2022.

### Organisations

## People |
## ORCID iD |

Nikolaos Constantinou (Student) |

### Studentship Projects

Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|

EP/W523793/1 | 30/09/2021 | 29/09/2025 | |||

2585621 | Studentship | EP/W523793/1 | 03/10/2021 | 29/09/2025 | Nikolaos Constantinou |