Optimal Management of a Variable Annuity Invested in a Black-Scholes Market Driven by a Multidimensional Fractional Brownian Motion

摘要

This article considers a defined-contribution pension scheme. It focuses in the post-retirement period and investigates the problem of controlling the level of payment of a variable annuity. The general version of the model is solved assuming a vector control variable differentiating the payments for each pensioner according to his age and an enhanced version for the market behavior, modeled via a multidimensional correlated fractional Brownian motion. Then, a reduced version of the basic model is also examined assuming an identical payment rate for all pensioners and a modified version of the typical Black-Scholes model driven by a standard fractional Brownian motion. Finally, a numerical application is developed for investigating the different investment strategies and also exploring the impact of the Hurst exponent in the final formula.View full textDownload full textKeywordsDefined-contribution pension schemes, Fractional Brownian motion (FBM), Riccati equation, Stochastic linear-quadratic (SLQ) control, Variable annuitiesMathematics Subject Classification93E20, 60E15, 60E44Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/07362994.2011.532021