Donnelly, Catherine

Heunis, Andrew

English

We study a problem of stochastic control in mathematical finance, for which the asset prices are modeled by Ito processes. The market parameters exhibit "regime-switching" in the sense of being adapted to the joint filtration of the Brownian motion in the asset price models and a given finite-state Markov chain which models"\regimes" of the market. The goal is to minimize a general quadratic loss function of the wealth at close of trade subject to the constraint that the vector of dollar amounts in each stock remains within a given closed convex set. We apply a conjugate duality approach, the essence of which is to establish existence of a solution to an associated dual problem and then use optimality relations to construct an optimal portfolio in terms of this solution. The optimality relations are also used to compute explicit optimal portfolios for various convex cone constraints when the market parameters are adapted specifically to the Markov chain

Heriot Watt Pure

Quadratic risk minimization in a regime-switching model with portfolio constraints

Catherine Donnelly

Andrew J. Heunis

Crossref

SIAM Journal on Control and Optimization

Quadratic Risk Minimization in a Regime-Switching Model with Portfolio Constraints

A martingale representation theorem for two independent semimartingales. Stochastics and Stochastic Reports,

Brownian motion and stochastic calculus.

Conjugate convex functions in optimal stochastic control.

Continuous Martingales and Brownian Motion.

Convex Analysis and Variational Problems.

Convex duality in constrained portfolio optimization.

Double martingales. Zeitschrift f ur Wahrscheinlichkeitstheorie und verwandte Gebiete,

Explicit solutions of consumption-investment problems in nancial markets with regime switching.

Foundations of Modern Probability.

Fundamentals of Convex Analysis.

Lectures from Markov Processes to Brownian Motion.

Limit Theorems for Stochastic Processes.

Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model.

Markowitz's portfolio optimization in an incomplete market.

Methods of Mathematical Finance.

Theory of Martingales.

Quadratic risk minimization in a regime-switching model with portfolio constraints

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Heriot Watt Pure

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Heriot Watt Pure