# On Regularity of Primal and Dual Dynamic Value Functions Related to Investment Problems and Their Representations as Backward Stochastic PDE Solutions

@article{Mania2017OnRO, title={On Regularity of Primal and Dual Dynamic Value Functions Related to Investment Problems and Their Representations as Backward Stochastic PDE Solutions}, author={M. Mania and R. Tevzadze}, journal={SIAM J. Financial Math.}, year={2017}, volume={8}, pages={483-503} }

We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximization problems are established. These properties are used to show that the value function satisfies a corresponding backward stochastic partial differential equation. In the case… Expand

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Forward BSDEs and backward SPDEs for utility maximization under endogenous pricing

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- 2020

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#### References

SHOWING 1-10 OF 18 REFERENCES

Backward stochastic partial differential equations related to utility maximization and hedging

- Mathematics
- 2008

We study the utility maximization problem, the problem of minimization of the hedging error and the corresponding dual problems using dynamic programming approach. We consider an incomplete financial… Expand

Backward stochastic PDEs related to the utility maximization problem

- Mathematics
- 2008

Abstract We study utility maximization problem for general utility functions using the dynamic programming approach. An incomplete financial market model is considered, where the dynamics of asset… Expand

On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets

- Mathematics, Economics
- 2006

We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also… Expand

On the properties of dynamic value functions in the problem of optimal investment in incomplete markets

- Mathematics
- 2015

Abstract We study the analytical properties of a dynamic value function and of an optimal solution to the utility maximization problem in incomplete markets for utility functions defined on the whole… Expand

The asymptotic elasticity of utility functions and optimal investment in incomplete markets

- Mathematics
- 1999

The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and… Expand

BACKWARD STOCHASTIC PDE AND IMPERFECT HEDGING

- Economics
- 2003

We consider a problem of minimization of a hedging error, measured by a positive convex random function, in an incomplete financial market model, where the dynamics of asset prices is given by… Expand

Forward-backward systems for expected utility maximization

- Mathematics
- 2011

In this paper we deal with the utility maximization problem with general utility functions including power utility with liability. We derive a new approach in which we reduce the resulting control… Expand

On the Existence of Minimax Martingale Measures

- Economics
- 2002

Embedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be an… Expand

A super-martingale property of the optimal portfolio process

- Economics, Computer Science
- Finance Stochastics
- 2003

Abstract. We show that, for a utility function having reasonable asymptotic elasticity , the optimal investment process is a super-martingale under each equivalent martingale measure , such that ,… Expand

An Exact Connection between Two Solvable SDEs and a Nonlinear Utility Stochastic PDE

- Mathematics, Computer Science
- SIAM J. Financial Math.
- 2013

This new approach addresses several issues with a new perspective: dynamic programming principle, risk tolerance properties, inverse problems, and focuses on the marginal utility SPDE by showing that it belongs to the previous family of SPDEs. Expand