scholarly journals ROBUST EXPONENTIAL HEDGING AND INDIFFERENCE VALUATION

2010 ◽  
Vol 13 (07) ◽  
pp. 1075-1101 ◽  
Author(s):  
KEITA OWARI
Keyword(s):  
Dual Problem ◽  
Maximization Problem ◽  
Probability Measures ◽  
Primal Problem ◽  
Robust Version ◽  
Indifference Valuation ◽  
Robust Utility Maximization ◽  
Indifference Price ◽  
Utility Indifference ◽  
Utility Maximization Problem

We discuss the problem of exponential hedging in the presence of model uncertainty expressed by a set of probability measures. This is a robust utility maximization problem with a contingent claim. We first consider the dual problem which is the minimization of penalized relative entropy over a product set of probability measures, showing the existence and variational characterizations of the solution. These results are applied to the primal problem. Then we consider the robust version of exponential utility indifference valuation, giving the representation of indifference price using a duality result.

scholarly journals Exponential utility indifference valuation in two Brownian settings with stochastic correlation

2008 ◽  
Vol 40 (2) ◽  
pp. 401-423 ◽  
Author(s):  
Christoph Frei ◽  
Martin Schweizer
Keyword(s):  
Monotonicity Property ◽  
Exponential Utility ◽  
Upper And Lower Bounds ◽  
Martingale Measure ◽  
Maximization Problem ◽  
Stochastic Correlation ◽  
Indifference Valuation ◽  
Random Endowment ◽  
Utility Indifference ◽  
Utility Maximization Problem

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the value VB of the exponential utility maximization problem with the claim B as random endowment. This yields an explicit formula for the indifference value b of B at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended. The reason why all this works is that, after a transformation to the minimal martingale measure, the value VB enjoys a monotonicity property in the correlation between tradable and nontradable assets.

scholarly journals Exponential utility indifference valuation in two Brownian settings with stochastic correlation

2008 ◽  
Vol 40 (02) ◽  
pp. 401-423
Author(s):  
Christoph Frei ◽  
Martin Schweizer
Keyword(s):  
Monotonicity Property ◽  
Exponential Utility ◽  
Upper And Lower Bounds ◽  
Martingale Measure ◽  
Maximization Problem ◽  
Stochastic Correlation ◽  
Indifference Valuation ◽  
Random Endowment ◽  
Utility Indifference ◽  
Utility Maximization Problem

We study the exponential utility indifference valuation of a contingent claimBin an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the valueVBof the exponential utility maximization problem with the claimBas random endowment. This yields an explicit formula for the indifference valuebofBat any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended. The reason why all this works is that, after a transformation to the minimal martingale measure, the valueVBenjoys a monotonicity property in the correlation between tradable and nontradable assets.

scholarly journals UTILITY THEORY FRONT TO BACK — INFERRING UTILITY FROM AGENTS' CHOICES

2014 ◽  
Vol 17 (03) ◽  
pp. 1450018 ◽  
Author(s):  
ALEXANDER M. G. COX ◽  
DAVID HOBSON ◽  
JAN OBłÓJ
Keyword(s):  
Utility Function ◽  
Utility Theory ◽  
Consistency Condition ◽  
Maximization Problem ◽  
Consumption Pattern ◽  
Investment Strategies ◽  
Inverse Approach ◽  
To Come ◽  
Utility Maximization Problem ◽  
Stochastic Setting

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behavior is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of a geometric Brownian motion market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximization problem. We show further that important characteristics of the agent such as risk attitudes (e.g., DARA) can be deduced directly from the agent's consumption and investment choices.

scholarly journals Dual Formulation of the Utility Maximization Problem Under Transaction Costs

2001 ◽  
Vol 11 (4) ◽  
pp. 1353-1383 ◽  
Author(s):  
Griselda Deelstra ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Maximization Problem ◽  
Dual Formulation ◽  
Utility Maximization Problem
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