# Sensitivity analysis of the utility maximisation problem with respect to model perturbations

@article{Mostovyi2017SensitivityAO, title={Sensitivity analysis of the utility maximisation problem with respect to model perturbations}, author={Oleksii Mostovyi and Mihai S{\^i}rbu}, journal={Finance and Stochastics}, year={2017}, volume={23}, pages={595-640} }

We consider the expected utility maximisation problem and its response to small changes in the market price of risk in a continuous semimartingale setting. Assuming that the preferences of a rational economic agent are modelled by a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and we construct trading strategies that match the indirect utility function up to the second order. The method, which is…

## 17 Citations

### Asymptotic analysis of the expected utility maximization problem with respect to perturbations of the numéraire

- MathematicsStochastic Processes and their Applications
- 2020

### Sensitivity analysis for expected utility maximization in incomplete Brownian market models

- MathematicsMathematics and Financial Economics
- 2018

We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, for…

### On the analyticity of the value function in optimal investment

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We study the analyticity of the value function in optimal investment with expected utility from terminal wealth. We identify both a class of utilities and a class of semi-martingale models for which…

### Utility Maximization Problem with Transaction Costs: Optimal Dual Processes and Stability

- Mathematics, EconomicsApplied Mathematics & Optimization
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In this paper, we investigate the stability problem of the numéraire-based utility maximization problem in markets with transaction costs, where the stock price is not necessarily a semimartingale.…

### A Sensitivity Analysis of the Long-Term Expected Utility of Optimal Portfolios

- EconomicsSSRN Electronic Journal
- 2019

This paper discusses the sensitivity of the long-term expected utility of optimal portfolios for an investor with constant relative risk aversion. Under an incomplete market given by a factor model,…

### A Free-Model Characterization of the Asymptotic Certainty Equivalent by the Arrow-Pratt Index

- EconomicsModeling, Stochastic Control, Optimization, and Applications
- 2019

This work concerns with the asymptotic behavior of the optimal wealth process, measured through the certainty equivalent of utility functions with convergent Arrow-Pratt risk aversion index, which we…

### Convergence of Optimal Expected Utility for a Sequence of Discrete-Time Market

- Mathematics, EconomicsSSRN Electronic Journal
- 2019

We examine Kreps’ (2019) conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies…

### Convergence of optimal expected utility for a sequence of discrete‐time markets

- Mathematics, EconomicsMathematical finance
- 2020

Kreps' conjecture is confirmed if the consumer's utility function U has asymptotic elasticity strictly less than one, and a counterexample to the conjecture is provided for a utilityfunction U with asymptic elasticity equal to 1, for ζ such that E[ζ3]>0.

### Convergence of optimal expected utility for a sequence of binomial models

- MathematicsMathematical finance
- 2021

We consider the convergence of the solution of a discrete‐time utility maximization problem for a sequence of binomial models to the Black‐Scholes‐Merton model for general utility functions. In…

### Continuity of utility maximization under weak convergence

- Economics, MathematicsMathematics and Financial Economics
- 2020

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the…

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