Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem

Levon Avanesyan (), Mykhaylo Shkolnikov () and Ronnie Sircar ()
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Levon Avanesyan: Princeton University
Mykhaylo Shkolnikov: Princeton University
Ronnie Sircar: Princeton University

Finance and Stochastics, 2020, vol. 24, issue 4, No 5, 1011 pages

Abstract: Abstract We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. Given multiple traded assets, the prices of which depend on multiple observable stochastic factors, we construct a large class of forward performance processes, as well as the corresponding optimal portfolios, with power-utility initial data and for stock–factor correlation matrices with eigenvalue equality (EVE) structure, which we introduce here. This is done by solving the associated nonlinear parabolic partial differential equations (PDEs) posed in the “wrong” time direction. Along the way, we establish on domains an explicit form of the generalised Widder theorem of Nadtochiy and Tehranchi (Math. Finance 27:438–470, 2015, Theorem 3.12) and rely for that on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the “right” time direction.

Keywords: Factor models; Forward performance processes; Generalised Widder theorem; Hamilton–Jacobi–Bellman equations; Ill-posed partial differential equations; Incomplete markets; Merton problem; Optimal portfolio selection; Positive eigenfunctions; Time-consistency; 35K55; 91G10; 35J15; 60H10 (search for similar items in EconPapers)
JEL-codes: C02 G11 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s00780-020-00436-1

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