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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)981-1011
Number of pages31
JournalFinance and Stochastics
Volume24
Issue number4
DOIs
StatePublished - Oct 1 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

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

Fingerprint Dive into the research topics of 'Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem'. Together they form a unique fingerprint.

Cite this