Characterisation of optimal dual measures via distortion
نویسندگان
چکیده
We derive representations for optimal martingale measures in a two-factor Markovian model, by seeking ramifications of a distortion power solution (Zariphopoulou (2001)) of the primal utility maximisation problem, for the dual problem. This provides an alternative to existing methods in the literature for characterising optimal measures, and gives new results in the form of a novel representation for the dual stochastic control problem, and in the form of Esscher transform relations between the optimal measure and the minimal measure. Journal of Economic Literature Classification: C61, D52, G11, G13 Mathematics Subject Classification (2000): 58J37, 60H30, 93E20
منابع مشابه
Characterization of optimal dual measures via distortion
We derive representations for the optimal dual martingale measure Q∗ associated with the dual to a primal utility maximization problem in a class of incomplete diffusion models containing a traded stock and a non-traded correlated stochastic factor. Using a distortion power solution [29] for the primal problem, an explicit solution is obtained for the dual value function, yielding representatio...
متن کاملRisk Redistribution with Distortion Risk Measures∗
This paper studies optimal risk redistribution between firms, such as banks or insurance companies. The introduction of the Basel II regulation and the Swiss Solvency Test (SST) has increased the use of risk measures to evaluate financial or insurance risk. We consider the case where firms use a distortion risk measure (also called dual utility) to evaluate risk. The paper first characterizes a...
متن کاملMartingale Methods in Dynamic Portfolio Allocation with Distortion Operators∗
Standard optimal portfolio choice models assume that investors maximise the expected utility of their future outcomes. However, behaviour which is inconsistent with the expected utility theory has often been observed. In a discrete time setting, we provide a formal treatment of risk measures based on distortion functions that are consistent with Yaari’s dual (non-expected utility) theory of cho...
متن کاملLow Resolution Scalar Quantization for Gaussian and Laplacian Sources with Absolute and Squared Error Distortion Measures
This report considers low resolution scalar quantization. Specifically, it considers entropyconstrained scalar quantization for memoryless Gaussian and Laplacian sources with both squared and absolute error distortion measures. The slope of the operational rate-distortion functions of scalar quantization for these sources and distortion measures is found. It is shown that in three of the four c...
متن کاملA Variational Approach to Nonlinear Estimation
We consider estimation problems, in which the estimand, X, and observation, Y , take values in measurable spaces. Regular conditional versions of the forward and inverse Bayes formula are shown to have dual variational characterisations involving the minimisation of an apparent information, and the maximisation of a compatible information. These both have natural information theoretic interpret...
متن کامل