On Near-optimal Necessary and Sufficient Conditions for Forward-backward Stochastic Systems with Jumps, with Applications to Finance

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F14%3A00209299" target="_blank" >RIV/68407700:21340/14:00209299 - isvavai.cz</a>

Výsledek na webu

<a href="http://am.math.cas.cz/full/59/4/am59_4_4.pdf" target="_blank" >http://am.math.cas.cz/full/59/4/am59_4_4.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10492-014-0064-4" target="_blank" >10.1007/s10492-014-0064-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Near-optimal Necessary and Sufficient Conditions for Forward-backward Stochastic Systems with Jumps, with Applications to Finance

Popis výsledku v původním jazyce

In this paper, we establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by Forward-backward stochas- tic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near-optimality. At the end, as an application to finance, mean-variance portfolio selection mixed with a recursive utility optimization problem is given.

Název v anglickém jazyce

On Near-optimal Necessary and Sufficient Conditions for Forward-backward Stochastic Systems with Jumps, with Applications to Finance

Popis výsledku anglicky

In this paper, we establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by Forward-backward stochas- tic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near-optimality. At the end, as an application to finance, mean-variance portfolio selection mixed with a recursive utility optimization problem is given.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

59

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

34

Strana od-do

407-440

Kód UT WoS článku

000339821600004

EID výsledku v databázi Scopus

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