Closed-form Solutions to Discrete-time Portfolio Optimization Problems
نویسنده
چکیده
In this paper, we study some discrete-time portfolio optimization problems. We introduce a discrete-time financial market model. The change in asset prices is modelled in contrast to the continuous-time market model by stochastic difference equations. We provide solutions of these stochastic difference equations. Then we introduce the discrete-time risk measures and the portfolio optimization problems. The main contributions of this paper are the closed-form solutions to the discrete-time portfolio models. For simulation purposes, the discrete-time financial market is often better suited. Several examples illustrating our theoretical results are provided.
منابع مشابه
A novel technique for a class of singular boundary value problems
In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...
متن کاملAsset Allocation under Imperfect Information: Closed-Form Consumption and Portfolio Choice under Incomplete Markets
This paper studies consumption and portfolio choice under incomplete markets and parameter uncertainty. I establish the necessary conditions under which the investor’s optimization problem under incomplete markets can be transformed into a complete markets problem. This paper extends the literature on asset allocation by obtaining closed form solutions to the consumption and portfolio problem o...
متن کاملPareto-optimal Solutions for Multi-objective Optimal Control Problems using Hybrid IWO/PSO Algorithm
Heuristic optimization provides a robust and efficient approach for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. The convergence rate and suitable diversity of solutions are of great importance for multi-objective evolutionary algorithms. The focu...
متن کاملOverview of Portfolio Optimization Models
Finding the best way to optimize the portfolio after Markowitz's 1952 article has always been and will continue to be one of the concerns of activists in the investment management industry. Researchers have come up with different solutions to overcome this problem. The introduction of mathematical models and meta-heuristic models is one of the activities that has influenced portfolio optimizati...
متن کاملModeling a Risk - Based Criterion for a Portfolio with Options ∗
The presence of options in a portfolio fundamentally alters the portfolio’s risk and return profiles when compared to an all equity portfolio. In this paper, we advocate modeling a risk-based criterion for optioned portfolio selection and rebalancing problems. The criterion is inspired by Chicago Mercantile Exchange’s risk-based margining system which sets the collateralization requirements on ...
متن کامل