scholarly journals Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Peng Yang
Keyword(s):  
Probability Measure ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Control Technique ◽  
Model Parameters ◽  
Cev Model ◽  
Terminal Wealth ◽  
Optimal Investment Strategy

A robust time-consistent optimal investment strategy selection problem under inflation influence is investigated in this article. The investor may invest his wealth in a financial market, with the aim of increasing wealth. The financial market includes one risk-free asset, one risky asset, and one inflation-indexed bond. The price process of the risky asset is governed by a constant elasticity of variance (CEV) model. The investor is ambiguity-averse; he doubts about the model setting under the original probability measure. To dispel this concern, he seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. The objective of the investor is to seek a time-consistent strategy so as to maximize his expected terminal wealth meanwhile minimizing his variance of the terminal wealth in the worst-case scenario. By using the stochastic optimal control technique, we derive closed-form solutions for the optimal time-consistent investment strategy, the probability scenario, and the value function. Finally, the influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments.

scholarly journals Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong He ◽  
Peimin Chen
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Stochastic Interest Rate ◽  
Model Parameters ◽  
Optimal Investment Strategy ◽  
Stochastic Interest ◽  
Cev Process ◽  
The Interest Rate

Interest rate is an important macrofactor that affects asset prices in the financial market. As the interest rate in the real market has the property of fluctuation, it might lead to a great bias in asset allocation if we only view the interest rate as a constant in portfolio management. In this paper, we mainly study an optimal investment strategy problem by employing a constant elasticity of variance (CEV) process and stochastic interest rate. The assets of investment for individuals are supposed to be composed of one risk-free asset and one risky asset. The interest rate for risk-free asset is assumed to follow the Cox–Ingersoll–Ross (CIR) process, and the price of risky asset follows the CEV process. The objective is to maximize the expected utility of terminal wealth. By applying the dual method, Legendre transformation, and asymptotic expansion approach, we successfully obtain an asymptotic solution for the optimal investment strategy under constant absolute risk aversion (CARA) utility function. In the end, some numerical examples are provided to support our theoretical results and to illustrate the effect of stochastic interest rates and some other model parameters on the optimal investment strategy.

scholarly journals Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1610
Author(s):  
Katia Colaneri ◽  
Alessandra Cretarola ◽  
Benedetta Salterini
Keyword(s):  
Stock Prices ◽  
Regime Switching ◽  
Common Factor ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Investment Strategy

In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

2012 ◽  
Vol 13 (2) ◽  
pp. 228-240 ◽  
Author(s):  
G. Bamberg ◽  
A. Neuhierl
Keyword(s):  
Heavy Tails ◽  
Geometric Mean ◽  
Asymptotic Optimality ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Optimal Investment Strategy ◽  
Optimality Properties ◽  
Heavy Tailed ◽  
The Impact

Abstract The strategy to maximize the long-term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two-asset economy with one risky asset and a risk-free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy-tailed log returns than for light-tailed log returns.

scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

MINIMIZING THE PROBABILITY OF LIFETIME RUIN: TWO RISKLESS ASSETS WITH TRANSACTION COSTS

2019 ◽  
Vol 49 (03) ◽  
pp. 847-883
Author(s):  
Xiaoqing Liang ◽  
Virginia R. Young
Keyword(s):  
Transaction Costs ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Money Market ◽  
The Other ◽  
Proportional Transaction Costs ◽  
Optimal Investment Strategy ◽  
The Individual ◽  
Riskless Asset

AbstractWe compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds are subject to proportional transaction costs. We consider the following three cases. (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

scholarly journals Dynamic Index Optimal Investment Strategy Based on Stochastic Differential Equations in Financial Market Options

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Financial Market ◽  
Capital Investment ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Insurance Companies ◽  
Investment Efficiency ◽  
Bank Deposits ◽  
Optimal Investment Strategy

With the gradual development and improvement of the financial market, financial derivatives such as futures and options have also become the objects of competition in the financial market. Therefore, how to make the most favorable and optimized investment and consumption when options are included? It has become a problem facing investors. Aiming at the optimal investment problem of investors, this paper studies the calculation of an optimal investment strategy in stochastic differential equations in financial market options on the basis of fuzzy theory. Now, stochastic calculus has become an important branch of stochastic analysis, finance, control, and other fields. The study of introducing stochastic differential equations is mainly to solve the stochastic control problem, which is the principle of the stochastic maximum. In finance, some hedging or pricing problems of contingent rights can eventually be transformed into a series of stochastic differential equations. Based on the historical data of five aspects of bank deposits, bonds, funds, stocks, and real estate of four listed insurance companies, the paper analyzes the optimization strategy of the capital investment of listed insurance companies based on the investment yield of the domestic investment market. According to the final results, the historical proportion of bank deposits of the superior company is 27%, and the optimal proportion given by the model is 25%; the total proportion of funds and stocks is 15%, and the optimal proportion of funds analyzed in the model is 20% and the optimal proportion of stocks is 10%. Therefore, the final results show that the investment efficiency of listed insurance companies can actually increase investment in stocks and funds and reduce the proportion of bank deposits to obtain greater investment returns.

Worst-Case Investment Strategy with Delay

2018 ◽  
Vol 6 (1) ◽  
pp. 35-57
Author(s):  
Chunxiang A ◽  
Yi Shao
Keyword(s):  
Financial Market ◽  
Normal State ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Model Parameters ◽  
Investment Strategies ◽  
Case Scenario ◽  
Worst Case ◽  
Risky Assets ◽  
Investment Optimization

AbstractThis paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.

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