Conditions for optimality in the infinite-horizon portfolio-cum-saving problem with semimartingale investments

Lucien Foldes

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Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

Abstract

A model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time is formulated in which the vector process representing returns to investments isa general semimartingale. Methods of stochastic calculus and calculus of variations are used to obtain necessary and sufficient conditions for optimality involving martingale properties ofthe shadow price processes associated with alternative portfolio cum saving plans.The relationship between such conditions and portfolio equations is investigated.The results are appliedtospecial cases where the returns process has stationary independent increments and the utility function has the discounted relative risk aversion form

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References

1971Optimum consumption and portfolio rules in a continuous-time model 1981Martingales and stochastic integrals in the theory of continuous trading 2013The Theory of Political Economy 1985An Intertemporal General Equilibrium Model of Asset Prices 1989Optimal consumption and portfolio policies when asset prices follow a diffusion process 1979Calcul Stochastique et Problèmes de Martingales 1987Optimal Portfolio and Consumption Decisions for a “Small Investor” on a Finite Horizon 1986A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios

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2011POWER UTILITY MAXIMIZATION IN CONSTRAINED EXPONENTIAL LÉVY MODELS 2000Valuation and martingale properties of shadow prices: An exposition 2004Utility Maximisation in Incomplete Markets 2004Portfolio optimization in incomplete financial markets

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