A CHANCE-CONSTRAINED PORTFOLIO SELECTION PROBLEM UNDER t-DISTRIBUTION

2007 ◽  
Vol 24 (04) ◽  
pp. 535-556 ◽  
Author(s):  
YI WANG ◽  
ZHIPING CHEN ◽  
KECUN ZHANG
Keyword(s):  
Stock Returns ◽  
Portfolio Selection ◽  
Asset Allocation ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Chance Constraint ◽  
Model Parameters ◽  
Allocation Model ◽  
Second Order Cone ◽  
T Distribution

Aimed at better modeling stock returns and finding robustly optimal investment decisions, a new portfolio selection model is proposed in this paper. The model differs from existing ones in following ways: multiple market frictions are taken into account simultaneously; the adopted multivariate t-distribution can capture the well-recognized fat tails in the return data by adding only one more parameter relative to the normal; the downside loss risk is controlled by a chance constraint which, including VaR as a special case, is flexible in terms of adjusting the threshold return and the loss probability level; one important advantage about the combination of the latter two innovations is that the derived asset allocation model can be transformed into a second-order cone program or a linear program, which can be easily solved in polynomial time. Empirical results based on some S&P 500 component stocks not only demonstrate the practicality of our new model, but show how different model parameters could affect the optimal portfolio selection. This is very useful in guiding investors to choose a correct model and to find the investment strategy most suitable for their specific purpose.

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.

THE IMPACT OF SAVINGS WITHDRAWALS ON A BANKER’S CAPITAL HOLDINGS SUBJECT TO BASEL III ACCORD

2020 ◽  
Vol 15 (02) ◽  
pp. 2050006
Author(s):  
RYLE S. PERERA ◽  
KIMITOSHI SATO
Keyword(s):  
Stock Returns ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Short Selling ◽  
Terminal Condition ◽  
Capital Regulation ◽  
Basel Iii ◽  
Investment Strategies ◽  
The Impact ◽  
Mean Variance

In this paper, we analyze the impact of savings withdrawals on a bank’s capital holdings under Basel III capital regulation. We examine the interplay between savings withdrawals and the investment strategies of a bank, by extending the classical mean–variance paradigm to investigate the bankers optimal investment strategy. We solve this via an optimization problem under a mean–variance paradigm, subject to a quadratic optimization function which incorporates a running penalization cost alongside the terminal condition. By solving the Hamilton–Jacobi–Bellman (HJB) equation, we derive the closed-form expressions for the value function as well as the banker’s optimal investment strategies. Our study provides a novel insight into the way banks allocate their capital holdings by showing that in the presence of savings withdrawals, banks will increase their risk-free asset holdings to hedge against the forthcoming deposit withdrawals whilst facing short-selling constraints. Moreover, we show that if the savings depositors of the bank are more stock-active, an economic expansion will imply a greater reduction in bank savings. As a result, the banker will reduce his/her loan portfolio and will depend on high stock returns with short-selling constraints to conform to Basel III capital regulation.

The Optimization on the Expected Utility Portfolio Selection Model without Short Sales

2011 ◽  
Vol 225-226 ◽  
pp. 1071-1074
Author(s):  
Peng Zhang ◽  
Hui Li Wang
Keyword(s):  
Portfolio Selection ◽  
Expected Utility ◽  
Risk Preference ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Selection Model ◽  
Short Sales ◽  
Expected Return ◽  
Portfolio Selection Model ◽  
Preference Coefficient

A new expected utility (EU) portfolio selection model without short sales is proposed. In the model, the expected utility function is quadratic. The model is solved by the pivoting algorithm. The paper showed in the EU portfolio selection model without the short sales, the relationship between the risk preference coefficient and the expected return is not linear but more complex. The risk preference coefficient could just reflect the investors’ preference in some intervals. We wrote program to calculate the optimal portfolios with the different coefficient. Investors could choose the optimal investment strategy according to both their own risk preference and the expected return of the portfolio.

Optimal investment-reinsurance problems with common shock dependent risks under two kinds of premium principles

2019 ◽  
Vol 53 (1) ◽  
pp. 179-206
Author(s):  
Junna Bi ◽  
Kailing Chen
Keyword(s):  
Risk Model ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Model Parameters ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Common Shock ◽  
The Impact ◽  
Poisson Risk Model

This paper considers the optimal investment-reinsurance strategy in a risk model with two dependent classes of insurance business under two kinds of premium principles, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the expected value premium principle and the variance premium principle, we use the stochastic optimal control theory to derive the optimal strategy and the value function for the compound Poisson risk model as well as for the Brownian motion diffusion risk model. In particular, we find that the optimal investment strategy on the risky asset is independent to the reinsurance strategy and the reinsurance strategy for the compound Poisson risk model are very different from those for the diffusion model under both two kinds of premium principles, but the investment strategies are the same in this two risk models. Finally, numerical examples are presented to show the impact of model parameters in the optimal strategies.

OPTIMAL INVESTMENT FOR A DEFINED-CONTRIBUTION PENSION SCHEME UNDER A REGIME SWITCHING MODEL

2015 ◽  
Vol 45 (2) ◽  
pp. 397-419 ◽  
Author(s):  
An Chen ◽  
Łukasz Delong
Keyword(s):  
Asset Allocation ◽  
Regime Switching ◽  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Switching Behavior ◽  
Pension Scheme ◽  
Defined Contribution ◽  
State Of The Economy ◽  
Plan Member

AbstractWe study an asset allocation problem for a defined-contribution (DC) pension scheme in its accumulation phase. We assume that the amount contributed to the pension fund by a pension plan member is coupled with the salary income which fluctuates randomly over time and contains both a hedgeable and non-hedgeable risk component. We consider an economy in which macroeconomic risks are existent. We assume that the economy can be in one ofIstates (regimes) and switches randomly between those states. The state of the economy affects the dynamics of the tradeable risky asset and the contribution process (the salary income of a pension plan member). To model the switching behavior of the economy we use a counting process with stochastic intensities. We find the investment strategy which maximizes the expected exponential utility of the discounted excess wealth over a target payment, e.g. a target lifetime annuity.

PORTFOLIO SELECTION BY MINIMIZING THE PRESENT VALUE OF CAPITAL INJECTION COSTS

2014 ◽  
Vol 45 (1) ◽  
pp. 207-238 ◽  
Author(s):  
Ming Zhou ◽  
Kam C. Yuen
Keyword(s):  
Portfolio Selection ◽  
Risk Model ◽  
Numerical Study ◽  
Optimal Investment ◽  
Investment Policy ◽  
Model Parameters ◽  
Capital Injection ◽  
Surplus Process ◽  
Insurance Portfolio ◽  
Special Cases

AbstractThis paper considers the portfolio selection and capital injection problem for a diffusion risk model within the classical Black–Scholes financial market. It is assumed that the original surplus process of an insurance portfolio is described by a drifted Brownian motion, and that the surplus can be invested in a risky asset and a risk-free asset. When the surplus hits zero, the company can inject capital to keep the surplus positive. In addition, it is assumed that both fixed and proportional costs are incurred upon each capital injection. Our objective is to minimize the expected value of the discounted capital injection costs by controlling the investment policy and the capital injection policy. We first prove the continuity of the value function and a verification theorem for the corresponding Hamilton–Jacobi–Bellman (HJB) equation. We then show that the optimal investment policy is a solution to a terminal value problem of an ordinary differential equation. In particular, explicit solutions are derived in some special cases and a series solution is obtained for the general case. Also, we propose a numerical method to solve the optimal investment and capital injection policies. Finally, a numerical study is carried out to illustrate the effect of the model parameters on the optimal policies.

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.

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 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.

RISK MANAGEMENT OF FINANCIAL CRISES: AN OPTIMAL INVESTMENT STRATEGY WITH MULTIVARIATE JUMP-DIFFUSION MODELS

2017 ◽  
Vol 47 (2) ◽  
pp. 501-525 ◽  
Author(s):  
Chou-Wen Wang ◽  
Hong-Chih Huang
Keyword(s):  
Risk Management ◽  
Financial Crisis ◽  
Asset Allocation ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Investment Strategy ◽  
Dependence Structure ◽  
Allocation Strategy ◽  
Investment Performance ◽  
Optimal Investment Strategy

AbstractThis paper provides an optimal asset allocation strategy to enhance risk management performance in the face of a financial crisis; this strategy entails constructing a good asset model – a multivariate jump-diffusion (MJD) model which includes idiosyncratic and systematic jumps simultaneously – and choosing suitable asset allocations and objective functions for fund management. This study also provides the dependence structure for the MJD model. The empirical implementation demonstrates that the proposed MJD model provides more detailed information about the financial crisis, allowing fund managers to determine an appropriate asset allocation strategy that enhances investment performance during the crisis.

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