Optimal Investment Strategy for DC Pension Plan with Stochastic Income and Inflation Risk under the Ornstein–Uhlenbeck Model

This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that the financial market consists of a risk-free asset and a risky asset, where the risky asset is subject to the Ornstein–Uhlenbeck (O-U) process, and stochastic income and inflation risk were also considered in the model. We firstly derived the Hamilton–Jacobi–Bellman (HJB) equation through the stochastic control method. Secondly, under the logarithmic utility function, the closed-form solution of optimal asset allocation was obtained by using the Legendre transform method. Finally, we give several numerical examples and a financial analysis.

Optimization of Capital Distribution and Composition of a Shipping Company Fleet Through Evolutionary Algorithms

The research examines the optimization of fleet management of a shipping company through control algorithms, as finding an algorithm that will reduce a marine company’s exposure to risk by diversifying its fleet composition is one way to make it dominant. The study focused on three companies that, in 2014, invested US$$1 billion in a fleet of tankers, using three different techniques to optimize their fleet composition: equal number of ships of all types, the established risk minimization model and the proposed Risky Asset Pricing maximization model. Seven years of data was used for the synthesis and 4 years of data was used for the evaluation. The research findings show that classic portfolio management through risk minimization is ineffective, as it appears to reduce performance below what is a random or evenly distributed fleet. Comparing the three methods, the superiority of the Risky Asset Pricing model is clear. This algorithm looks for solutions where the demand for ships is low but has enormous fluctuation potential and seeks to identify ships that are at high risk with great potential for price increases to maximize investor returns. The value of the research lies in the identification of methods to optimize capital distribution and composition of a shipping company fleet, which presents valuable insights for the benefit of scholars and maritime companies. Moreover, and contrary to extant works that focus on Markowitz’s theory, this article instead describes how evolutionary algorithms can be used to optimize fleet management.

On Calculating Method of the Kelly Criterion for Financial Investment in Single Risky Asset with Various Distributions of Returns

In this paper, the expectation of the reciprocal of first-degree polynomials of non-negative valued random variables is calculated. This is motivated to compute the Kelly criterion, which is the optimal solution of the maximization of the expected logarithm of the investment return. As soon as the expectation of the reciprocal of first-degree polynomials of asset returns is calculated, which is our main interest, the Kelly criterion can be obtained by using the ordinary optimization technique or applying the appropriate algorithm.

Value functions in a regime switching jump diffusion with delay market model

<abstract><p>In this paper, we consider a market model where the risky asset is a jump diffusion whose drift, volatility and jump coefficients are influenced by market regimes and history of the asset itself. Since the trajectory of the risky asset is discontinuous, we modify the delay variable so that it remains defined in this discontinuous setting. Instead of the actual path history of the risky asset, we consider the continuous approximation of its trajectory. With this modification, the delay variable, which is a sliding average of past values of the risky asset, no longer breaks down. We then use the resulting stochastic process in formulating the state variable of a portfolio optimization problem. In this formulation, we obtain the dynamic programming principle and Hamilton Jacobi Bellman equation. We also provide a verification theorem to guarantee the optimal solution of the corresponding stochastic optimization problem. We solve the resulting finite time horizon control problem and show that close form solutions of the stochastic optimization problem exist for the cases of power and logarithmic utility functions. In particular, we show that the HJB equation for the power utility function is a first order linear partial differential equation while that of the logarithmic utility function is a linear ordinary differential equation.</p></abstract>

An exact and explicit formula for pricing lookback options with regime switching

<p style='text-indent:20px;'>This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on states of the economy described by a continuous-time Markov chain process. We derive an exact, explicit and closed-form solution for European-style lookback options in a two-state regime switching model.</p>