On Bellman's equations for mean and variance control of a Markov diffusion

European Journal of Operational Research

Palczewski

2014

This paper introduces a general continuous-time mathematical framework for solution of dynamic mean-variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean-variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme's symmetry on trading behaviour and fund performance.

Section: Mean-variance Optimization For Integral Functionalsmentioning

confidence: 91%

Section: Compensation Schemes Based On Continuously Monitored Performmentioning

confidence: 99%

“…Following Aivaliotis and Veretennikov [4] we propose an approach to reformulate this quadratic term. Fubini's theorem implies…”

Section: Mean-variance Optimization For Integral Functionalsmentioning

confidence: 99%

“…Using a dual representation x 2 = sup ψ∈R {−ψ 2 − 2ψx} (as in Aivaliotis and Veretennikov [4]), we rewrite the variance term:…”

Section: Mean-variance Optimization For Terminal-time Functionalsmentioning

confidence: 99%

See 2 more Smart Citations

Investment strategies and compensation of a mean–variance optimizing fund manager

European Journal of Operational Research

Palczewski

2014

“…With regards to the functional, the problem without a"final payment" Φ has been discussed in [1] with solutions in Sobolev spaces and the problems with either only integral functional or only "final payment" were discussed in [2] using Viscosity solutions. It is clear, however, that the solution to problem (2) cannot be derived as a combination of the previous two cases due to the supremum involved.…”

Section: Introductionmentioning

confidence: 99%

An HJB Approach to a General Continuous-Time Mean-Variance Stochastic Control Problem

Veretennikov

2015

SSRN Journal

A general continuous mean-variance problem is considered where the cost functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic optimization problems. The value function of the latter can be considered as the solution to a degenerate HJB equation either in viscosity or in Sobolev sense (after regularization) under suitable assumptions and with implications with regards to the optimality of strategies.

An HJB approach to a general continuous-time mean-variance stochastic control problem

Random Operators and Stochastic Equations

Veretennikov

2018

A general continuous mean-variance problem is considered for a diffusion controlled process where the reward functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic optimization problem. The value function of the latter can be considered as the solution to a degenerate HJB equation either in viscosity or in Sobolev sense (after a regularization) under suitable assumptions and with implications with regards to the optimality of strategies. There is a useful interplay between the two approaches -viscosity and Sobolev.