scholarly journals Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion

2021 ◽  
Author(s):  
Bohan Li ◽  
Junyi Guo
Keyword(s):  
Optimal Strategy ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Capital Asset Pricing ◽  
Investment Strategies ◽  
Asset Pricing Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Zero Sum ◽  
Mean Variance

This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.

Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market

2019 ◽  
Vol 53 (4) ◽  
pp. 1171-1186
Author(s):  
Reza Keykhaei
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Exit Time ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Homogeneous Markov Chain ◽  
Investment Strategies ◽  
Special Cases ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, we deal with multi-period mean-variance portfolio selection problems with an exogenous uncertain exit-time in a regime-switching market. The market is modelled by a non-homogeneous Markov chain in which the random returns of assets depend on the states of the market and investment time periods. Applying the Lagrange duality method, we derive explicit closed-form expressions for the optimal investment strategies and the efficient frontier. Also, we show that some known results in the literature can be obtained as special cases of our results. A numerical example is provided to illustrate the results.

On the Distribution of Terminal Wealth under Dynamic Mean-Variance Optimal Investment Strategies

2021 ◽  
Vol 12 (2) ◽  
pp. 566-603
Author(s):  
Pieter M. van Staden ◽  
Duy-Minh Dang ◽  
Peter A. Forsyth
Keyword(s):  
Optimal Investment ◽  
Investment Strategies ◽  
Terminal Wealth ◽  
Mean Variance

Average Drawdown Risk and Capital Asset Pricing

2013 ◽  
Vol 16 (04) ◽  
pp. 1350028 ◽  
Author(s):  
Mohammad Reza Tavakoli Baghdadabad ◽  
Paskalis Glabadanidis
Keyword(s):  
Asset Pricing ◽  
Mutual Funds ◽  
Risk Measure ◽  
Capital Asset Pricing ◽  
Pricing Model ◽  
Capital Asset ◽  
Acceptable Risk ◽  
Asset Pricing Model ◽  
The Past ◽  
Mean Variance

Practitioners and academics have spent the past few decades debating the validity and relevance of the capital asset pricing model (CAPM). One of the attributes of the model is an estimate of risk by beta, which in equilibrium describe the behavior of mean-variance (MV) investors. In the MV framework, risk is measured by the variance of returns which is a questionable and restrictive risk measure. In contrast, the average drawdown risk is a more acceptable risk measure and can be applied to modeling an alternative behavioral hypothesis, namely mean-drawdown behavior with a replacement risk measure for diversified investors, the average drawdown beta leading to an alternative pricing model based on this beta. Our findings clearly support the average drawdown beta and the pricing model of average drawdown CAPM versus the conventional beta and CAPM in a sample of Malaysian mutual funds.

DYNAMIC MEAN-VARIANCE OPTIMIZATION UNDER CLASSICAL RISK MODEL WITH FRACTIONAL BROWNIAN MOTION PERTURBATION

2008 ◽  
Vol 11 (04) ◽  
pp. 589-602 ◽  
Author(s):  
HUAYUE ZHANG ◽  
LIHUA BAI
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Risk Model ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Risk Process ◽  
Classical Risk Model ◽  
Classical Risk Process ◽  
Optimal Investment Problem ◽  
Mean Variance

In this paper, we apply the completion of squares method to study the optimal investment problem under mean-variance criteria for an insurer. The insurer's risk process is modelled by a classical risk process that is perturbed by a standard fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). By virtue of an auxiliary process, the efficient strategy and efficient frontier are obtained. Moreover, when H → 1/2+ the results converge to the corresponding (known) results for standard Brownian motion.

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.

CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING

2019 ◽  
Vol 22 (06) ◽  
pp. 1950029
Author(s):  
ZHIPING CHEN ◽  
LIYUAN WANG ◽  
PING CHEN ◽  
HAIXIANG YAO
Keyword(s):  
Brownian Motion ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Defined Contribution ◽  
Risky Assets ◽  
Mean Variance Portfolio ◽  
Mean Variance

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

scholarly journals Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Jingyun Sun ◽  
Zhongfei Li ◽  
Yongwu Li
Keyword(s):  
Pension Plan ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Value Functions ◽  
Defined Contribution ◽  
Hjb Equations ◽  
Plan Member ◽  
The Mean ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

We consider a portfolio selection problem for a defined contribution (DC) pension plan under the mean-variance criteria. We take into account the inflation risk and assume that the salary income process of the pension plan member is stochastic. Furthermore, the financial market consists of a risk-free asset, an inflation-linked bond, and a risky asset with Heston’s stochastic volatility (SV). Under the framework of game theory, we derive two extended Hamilton-Jacobi-Bellman (HJB) equations systems and give the corresponding verification theorems in both the periods of accumulation and distribution of the DC pension plan. The explicit expressions of the equilibrium investment strategies, corresponding equilibrium value functions, and the efficient frontiers are also obtained. Finally, some numerical simulations and sensitivity analysis are presented to verify our theoretical results.

scholarly journals Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chubing Zhang
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Pension Funds ◽  
Form Solution ◽  
Defined Contribution ◽  
Time Dynamic ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

scholarly journals Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chubing Zhang ◽  
Ximing Rong
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Plan Member ◽  
Cara Utility ◽  
Hamilton Jacobi Bellman ◽  
Coupon Bond

We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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