2010/05/24 by Łukasz Delong, Delong, Lukasz · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1005.4417
openalex publication_date 2010/05/24 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
In this paper we investigate novel applications of a new class of equations\nwhich we call time-delayed backward stochastic differential equations.\nTime-delayed BSDEs may arise in finance when we want to find an investment\nstrategy and an investment portfolio which should replicate a liability or meet\na target depending on the applied strategy or the past values of the portfolio.\nIn this setting, a managed investment portfolio serves simultaneously as the\nunderlying security on which the liability/target is contingent and as a\nreplicating portfolio for that liability/target. This is usually the case for\ncapital-protected investments and performance-linked pay-offs. We give examples\nof pricing, hedging and portfolio management problems (asset-liability\nmanagement problems) which could be investigated in the framework of\ntime-delayed BSDEs. Our motivation comes from life insurance and we focus on\nparticipating contracts and variable annuities. We derive the corresponding\ntime-delayed BSDEs and solve them explicitly or at least provide hints how to\nsolve them numerically. We give a financial interpretation of the theoretical\nfact that a time-delayed BSDE may not have a solution or may have multiple\nsolutions.\n