Optimization of Generalized Certainty Equivalents on the Finite Horizon

Year 2023, Volume: 4 Issue: 1, 116 - 133, 26.06.2023

Arnab Basu

https://doi.org/10.55546/jmm.1248851

Abstract

This paper addresses some open issues in optimization of generic certainty equivalents. Such equivalents have been modelled using increasing functionals of the discounted sums of the per-stage unbounded-above cost or reward functions defined on the paths of the underlying controlled Markov chain on general state spaces which models the random dynamics of the system. Examples of such functionals include logarithmic and power utilities as well as the robust Risk-Sensitive preferences among others. The critical results that were obtained were the solutions of this problem for generic unbounded-above per-stage cost minimization and for per stage reward maximization, both satisfying a w-growth (hence unbounded) condition in the nite horizon setup. In the process, we establish certain nontrivial closure properties of the dynamic programming operators. In addition, we provide a real-life example from Portfolio Consumption.

Keywords

Certainty equivalents, Full-path accummulated setup, Unbounded rewards and costs, Discounted path sums, Robust or risk-sensitive preferences

Thanks

The author most sincerely thanks Prof. Dr. Sukru Talas for his kind support in typesetting and formatting this manuscript as per the requirements of this journal.

Sonlu Ufukta Genelleştirilmiş Kesinlik Eşdeğerlerinin Optimizasyonu

Abstract

Bu makale, jenerik kesinlik eşdeğerlerinin optimizasyonundaki bazı açık sorunları ele almaktadır. Bu tür eşdeğerler, sistemin rasgele dinamiklerini modelleyen genel durum uzaylarında altta yatan kontrollü Markov zincirinin yollarında tanımlanan aşama başına sınırsız-üstü maliyet veya ödül fonksiyonlarının iskonto edilmiş toplamlarının artan fonksiyonelleri kullanılarak modellenmiştir. Bu tür işlevselliklere örnek olarak logaritmik ve güç araçlarının yanı sıra diğerleri arasında sağlam Riske Duyarlı tercihler verilebilir. Elde edilen kritik sonuçlar, her ikisi de gece ufku kurulumunda bir w-büyüme (dolayısıyla sınırsız) koşulunu sağlayan genel sınırsız-aşama üstü maliyet minimizasyonu ve aşama başına ödül maksimizasyonu için bu problemin çözümleriydi. Bu süreçte, dinamik programlama işleçlerinin önemsiz olmayan belirli kapatma özelliklerini oluşturuyoruz. Ek olarak, Portföy Tüketiminden gerçek hayattan bir örnek sunuyoruz.

Keywords

Kesinlik eşdeğerleri, Tam Yol Birikmiş Kurulum, Sınırsız ödüller ve maliyetler, İndirimli yol toplamları, Sağlam veya riske duyarlı terçihler

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