Dynamic exponential utility indifference valuation

By Michael Mania, Martin Schweizer. 2005

213 citations recorded by the source corpus.

We study the dynamics of the exponential utility indifference value process C(B;\alpha) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B;\alpha) is (the first component of) the unique solution of a backward stochastic differential equation with a quadratic generator and obtain BMO estimates for the components of this solution. This allows us to prove several new results about C_t(B;\alpha). We obtain continuity in B and local Lipschitz-continuity in the risk aversion \alpha, uniformly in t, and we extend earlier results on the asymptotic behavior as \alpha\searrow0 or \alpha\nearrow\infty to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/66d979ce7151373e6ec4f1e3cfac0f5b69deb7ba

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Citations in the corpus

7 – Backward Stochastic Differential Equations (2011, unknown): “Mania and Schweizer [60] and Ankirchner et al.”
Multidimensional quadratic and subquadratic BSDEs with special structure (2013, background): “Mania and Schweizer [14] and Ankirchner et al. [1] studied the transformation of one-dimensional quadratic BSDEs under a change of measure, but not with the aim of proving the existence of a classical solution.”
Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition (2011, unknown): “es, for example, in the context of utility optimization problems with exponential utility functions, or alternatively in questions related to risk minimization for the entropic risk measure (see e.g. [27, 17, 24] among many other references). Many papers deal with existence and uniqueness of solutio”
Minimal Entropy Martingale Measure (2010, background): “This topic has first been studied in [4], [58], [59], [64]; later work has examined intertemporally dynamic extensions ([5], [51]), descriptions via BSDEs in specific models ([6], [51]), extensions to more general payoff structures ([38], [47], [48], [61]), etc.”
Dynamic risk measures (2010, background): “Remark 28.”
OPTIMAL INVESTMENT UNDER RELATIVE PERFORMANCE CONCERNS (2015, result): “3 The main results Similar to the classical literature on portfolio optimization with exponential utility (El Karoui and Rouge [14], Hu, Imkeller and Muller [21], Mania and Schweizer [33]), we first establish a connection between Nash equilibria and a quadratic multi-dimensional BSDE.”
Exponential utility maximization under model uncertainty for unbounded endowments (2016, background): “In case of exponential utility function (though in a continuous-time and non-robust setting) [19] and [13] were the first to prove duality and existence, which lead to further analysis, for example a BSDE characterization of the optimal value and solution in an incomplete market and under trading co”
Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging (2006, background): “9) of [21] for a general filtration, one sees that the λ-integral part of the generator in our BSDE (4.”
A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem (2010, methodology): “To handle this optimization problem, which is formulated at any time under a conditional form, the approach consists in using both the martingale optimality principle and BSDE techniques: this approach is the same as in the previous papers [BEC06], [ MS05 ] and [MOR08] already dealing with the same ”
A Stochastic Control Approach to a Robust Utility Maximization Problem (2007, result): “The BSDE (25) is very similar to an equation studied in detail in [15], but has a crucial difference: If the final value YT = α′U ′ T is unbounded, there is no evident way in which the results from [15] could be used or adapted.”
Conditional and dynamic convex risk measures (2005, background): “Mania and Schweizer [20] introduce an underlying incomplete market and study the dynamics of exponential utility indifferent prices, a notion which is strictly related to dynamic entropic risk measures.”
Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs (2011, background): “Some other authors have obtained further results in some particular situations (see for instance Hu & Schweizer [28], Hu, Imkeller & Muller[27], Mania and Tevzadze [36] or Delbaen, Hu & Richou [13]).”
Solvability of backward stochastic differential equations with quadratic growth (2007, unknown): “[14] Mania M. and Schweizer M., (2005) Dynamic exponential utility indifference valuation, Ann.”
Dynamic Monetary Risk Measures for Bounded Discrete-Time Processes (2004, background): “Conditional entropic risk measures and their dynamic properties are also studied in Frittelli and Rosazza Gianin (2004), Barrieu and El Karoui (2004), Mania and Schweizer (2005), and Detlefsen and Scanolo (2005).”