TY - JOUR
T1 - Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem
AU - Avanesyan, Levon
AU - Shkolnikov, Mykhaylo
AU - Sircar, Ronnie
N1 - Funding Information:
M. Shkolnikov was partially supported by the NSF grant DMS-1506290. L. Avanesyan was partially supported by a Gordon Y.S. Wu Fellowship in Engineering.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - 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.
AB - 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.
KW - Factor models
KW - Forward performance processes
KW - Generalised Widder theorem
KW - Hamilton–Jacobi–Bellman equations
KW - Ill-posed partial differential equations
KW - Incomplete markets
KW - Merton problem
KW - Optimal portfolio selection
KW - Positive eigenfunctions
KW - Time-consistency
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U2 - 10.1007/s00780-020-00436-1
DO - 10.1007/s00780-020-00436-1
M3 - Article
AN - SCOPUS:85090789969
SN - 0949-2984
VL - 24
SP - 981
EP - 1011
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 4
ER -