# Exponential Hedging and Entropic Penalties

@article{Delbaen2002ExponentialHA, title={Exponential Hedging and Entropic Penalties}, author={Freddy Delbaen and Peter Grandits and Thorsten Rheinl{\"a}nder and Dominick Samperi and Martin Schweizer and Ch. Stricker}, journal={Mathematical Finance}, year={2002}, volume={12} }

We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X. We prove a duality relation between this problem and a dual problem for local martingale measures Q for X where we either minimize relative entropy minus a correction term involving B or maximize the Q‐price of B subject to an entropic penalty term. Our result is robust in the sense that it holds for several choices of the space of…

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## References

SHOWING 1-10 OF 48 REFERENCES

On the Existence of Minimax Martingale Measures

- Mathematics, 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…

Pricing Via Utility Maximization and Entropy

- Economics
- 2000

In a financial market model with constraints on the portfolios, define the price for a claim C as the smallest real number p such that supπ E[U(XTx+p, π−C)]≥ supπ E[U(XTx, π)], where U is the…

Rational Hedging and Valuation with Utility-Based Preferences

- Economics, Mathematics
- 2001

Stochastic optimization problems in which concave functionals are maximized on spaces of stochastic integrals are studied in mathematical finance for a risk-averse investor who is faced with valuation, hedging, and optimal investment problems in incomplete financial markets.

Utility maximization in incomplete markets with random endowment

- Mathematics, EconomicsFinance Stochastics
- 2001

It is shown that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form of the regular part of an element of the dual space of ${\bf L}^\infty$.

A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios

- Economics, MathematicsMath. Oper. Res.
- 1986

The problem of choosing a portfolio of securities so as to maximize the expected utility of wealth at a terminal planning horizon is solved via stochastic calculus and convex analysis and a martingale representation problem is developed.

On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper

- Mathematics
- 2002

This note contains ramifications of results of Delbaen et al. (2002). Assuming that the price process is locally bounded and admits an equivalent local martingale measure with finite entropy, we…

Dynamic programming and mean-variance hedging

- MathematicsFinance Stochastics
- 1999

This paper obtains new explicit characterizations of hedging numéraire and the variance-optimal martingale measure in terms of the value function of a suitable stochastic control problem and derives an explicit form of this value function and then of the hedgingnuméraires and the Variance-Optimal martingsale measure.

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

- Economics, 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…

Minimax and minimal distance martingale measures and their relationship to portfolio optimization

- MathematicsFinance Stochastics
- 2001

It is shown that the minimal distance martingale measures are equivalent to minimax martingALE measures with respect to related utility functions and that optimal portfolios can be characterized by them.

Couverture des actifs contingents et prix maximum

- Mathematics, Economics
- 1994

The problem of pricing contingent claims from the price dynamics of some securities is well understood in the context of a complete financial market. In order to avoid any arbitrage opportunity, we…