Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty

Jean-Pierre Aubin, Dominique Pujal and Patrick Saint-Pierre

Chapter Chapter 3 in Numerical Methods in Finance, 2005, pp 59-89 from Springer

Abstract: Abstract We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very definition of the guaranteed valuation set can be formulated directly in terms of guaranteed viable-capture basin of a dynamical game. Hence, we shall “compute” the guaranteed viable-capture basin and find a formula for the valuation function involving an underlying criterion, use the tangential properties of such basins for proving that the valuation function is a solution to Hamilton-Jacobi-Isaacs partial differential equations. We then derive a dynamical feedback providing an adjustment law regulating the evolution of the portfolios obeying viability constraints until it achieves the given objective in finite time. We shall show that the Pujal—Saint-Pierre viability/capturability algorithm applied to this specific case provides both the valuation function and the associated portfolios.

Keywords: Variational Inequality; Transaction Cost; Option Price; Differential Inclusion; Risky Asset (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-25118-9_3

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DOI: 10.1007/0-387-25118-9_3

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