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 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 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 Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

2020 ◽  
Vol 45 (4) ◽  
pp. 1210-1236 ◽  
Author(s):  
Shuoqing Deng ◽  
Xiaolu Tan ◽  
Xiang Yu
Keyword(s):  
Dynamic Programming ◽  
Transaction Costs ◽  
Model Uncertainty ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Market Condition ◽  
Maximization Problem ◽  
Proportional Transaction Costs ◽  
Utility Indifference ◽  
Basic Features

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numéraire-based semistatic utility maximization problem with an exponential utility preference. The randomization techniques recently developed in Bouchard, Deng, and Tan [Bouchard B, Deng S, Tan X (2019) Super-replication with proportional transaction cost under model uncertainty. Math. Finance 29(3):837–860.], allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.], we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.] to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.

scholarly journals Dynamic exponential utility indifference valuation

2005 ◽  
Vol 15 (3) ◽  
pp. 2113-2143 ◽  
Author(s):  
Michael Mania ◽  
Martin Schweizer
Keyword(s):  
Exponential Utility ◽  
Indifference Valuation ◽  
Utility Indifference

OPTION PRICING FOR GARCH MODELS WITH MARKOV SWITCHING

2006 ◽  
Vol 09 (06) ◽  
pp. 825-841 ◽  
Author(s):  
ROBERT J. ELLIOTT ◽  
TAK KUEN SIU ◽  
LEUNGLUNG CHAN
Keyword(s):  
Markov Switching ◽  
Martingale Measure ◽  
Maximization Problem ◽  
Option Valuation ◽  
Chain Process ◽  
Esscher Transform ◽  
Actuarial Science ◽  
Power Utility ◽  
Alternative Approach ◽  
Utility Maximization Problem

In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one of the regimes described by the states of an observable Markov chain process. By augmenting the conditional Esscher transform with the observable Markov switching process, a Markov switching conditional Esscher transform (MSCET) is developed to identify a martingale measure for option valuation in the incomplete market described by our model. We provide an alternative approach for the derivation of an analytical option valuation formula under the Markov switching Heston-Nandi GARCH (1, 1) model. The use of the MSCET can be justified by considering a utility maximization problem with respect to a power utility function associated with the Markov switching risk-averse parameters.

scholarly journals Life Insurance and Subsistence Consumption with an Exponential Utility

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 358
Author(s):  
Ho-Seok Lee
Keyword(s):  
Mortality Risk ◽  
Life Insurance ◽  
Explicit Solution ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Maximization Problem ◽  
Duality Method ◽  
Utility Maximization Problem

In this paper, we derive an explicit solution to the utility maximization problem of an individual with mortality risk and subsistence consumption constraint. We adopt an exponential utility for the individual’s consumption and the martingale and duality method is employed. From the explicit solution, we exhibit how the mortality intensity and subsistence consumption constraint affect, separately and together, portfolio, consumption and life insurance purchase.

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