Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

Abstract

This paper is concerned with an investor trading in multiple securities over many time periods in order to meet an outstanding liability at some future date. The investor is concerned with maximizing the expected profits from portfolio rebalancing under an initial wealth restriction to meet the future liabilities. We formulate the problem as a discrete-time stochastic optimization model and allow asset prices to have continuous probability distributions on compact domains. For the case of Markovian price uncertainty and convex terminal liability, we develop a simplicial approximation, under which bounds on the problem can be computed efficiently. Computations only require evaluating a dynamic programming recursion, which thus, allows its application to problems with a large number of trading periods. The bounds are tight in that they are exact in certain cases. Numerical results are given to demonstrate the computational efficiency of the procedure.

The nested Sinkhorn divergence to learn the nested distance

“…The nested distance quantifies the distance of stochastic processes and multistage stochastic programs are continuous with respect to the nested distance. Multistage stochastic programming has applications in many sectors, e.g., the financial sector (Edirisinghe 2005;Brodt 1983), in management science or in energy economics (Analui and Pflug 2014;Beltrán et al 2017;Carpentier et al 2012Carpentier et al , 2015. The prices, demands, etc., are often modeled as a stochastic process ξ = (ξ 0 , .…”

Nested Sinkhorn Divergence To Compute The Nested Distance

“…The nested distance is employed in multistage stochastic programming to describe the quality of an approximation. Multistage stochastic programming has applications in many sectors, e.g., the financial sector (Edirisinghe [10], Brodt [6]), in management science or in energy economics (Analui and Pflug [1], Beltrán et al [3], Carpentier et al [7,8]). The prices, demands, etc., are often modeled as a stochastic process 𝜉 = (𝜉 0 , .…”

A Variance Multi-period Portfolio Model with Fixed Ratio Based on Ternary Interval Numbers

“…Chi Guotai et al [18] established a multi-period dynamic portfolio optimization model using the inverse recursive principle and the nonlinear programming method. Edirisinghe [19] was concerned with an investor trading in multiple securities over many time periods in order to meet an outstanding liability at some future date. Zhang Jinli et al [20] proposed a discrete-time version of dynamic portfolio selection model for survival in fuzzy environments.…”