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.

scholarly journals Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis

2008 ◽  
Vol 38 (2) ◽  
pp. 423-440 ◽  
Author(s):  
Ralf Korn ◽  
Anke Wiese
Keyword(s):  
Expected Utility ◽  
Ruin Probability ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Risk Process ◽  
Investment Strategies ◽  
Portfolio Strategies ◽  
Classical Risk Process ◽  
Portfolio Optimization Problem ◽  
Mean Variance

We study the continuous-time portfolio optimization problem of an insurer. The wealth of the insurer is given by a classical risk process plus gains from trading in a risky asset, modelled by a geometric Brownian motion. The insurer is not only interested in maximizing the expected utility of wealth but is also concerned about the ruin probability. We thus investigate the problem of optimizing the expected utility for a bounded ruin probability. The corresponding optimal strategy in various special classes of possible investment strategies will be calculated. For means of comparison we also calculate the related mean-variance optimal strategies.

scholarly journals Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis

2008 ◽  
Vol 38 (02) ◽  
pp. 423-440 ◽  
Author(s):  
Ralf Korn ◽  
Anke Wiese
Keyword(s):  
Expected Utility ◽  
Ruin Probability ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Risk Process ◽  
Investment Strategies ◽  
Portfolio Strategies ◽  
Classical Risk Process ◽  
Portfolio Optimization Problem ◽  
Mean Variance

We study the continuous-time portfolio optimization problem of an insurer. The wealth of the insurer is given by a classical risk process plus gains from trading in a risky asset, modelled by a geometric Brownian motion. The insurer is not only interested in maximizing the expected utility of wealth but is also concerned about the ruin probability. We thus investigate the problem of optimizing the expected utility for a bounded ruin probability. The corresponding optimal strategy in various special classes of possible investment strategies will be calculated. For means of comparison we also calculate the related mean-variance optimal strategies.

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.

scholarly journals High-frequency trading with fractional Brownian motion

2020 ◽  
Author(s):  
Paolo Guasoni ◽  
Yuliya Mishura ◽  
Miklós Rásonyi
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
High Frequency ◽  
Asset Price ◽  
Optimal Strategies ◽  
Trading Costs ◽  
Frequency Limit ◽  
Dynamic Optimisation ◽  
High Frequency Limit ◽  
Mean Variance

Abstract In the high-frequency limit, conditionally expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon and making dynamic optimisation problems tractable. We find an explicit formula for locally mean–variance optimal strategies and their performance for an asset price that follows fractional Brownian motion. Without trading costs, risk-adjusted profits are linear in the trading horizon and rise asymmetrically as the Hurst exponent departs from Brownian motion, remaining finite as the exponent reaches zero while diverging as it approaches one. Trading costs penalise numerous portfolio updates from short-lived signals, leading to a finite trading frequency, which can be chosen so that the effect of trading costs is arbitrarily small, depending on the required speed of convergence to the high-frequency limit.

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.

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 On Risk Model with Dividends Payments Perturbed by a Brownian Motion – An Algorithmic Approach

2008 ◽  
Vol 38 (1) ◽  
pp. 183-206 ◽  
Author(s):  
Esther Frostig
Keyword(s):  
Brownian Motion ◽  
Risk Model ◽  
Risk Process ◽  
Insurance Company ◽  
Algorithmic Approach ◽  
Compound Poisson ◽  
Expected Time ◽  
Premium Rate ◽  
Surplus Process ◽  
Phase Type

Assume that an insurance company pays dividends to its shareholders whenever the surplus process is above a given threshold. In this paper we study the expected amount of dividends paid, and the expected time to ruin in the compound Poisson risk process perturbed by a Brownian motion. Two models are considered: In the first one the insurance company pays whatever amount exceeds a given level b as dividends to its shareholders. In the second model, the company starts to pay dividends at a given rate, smaller than the premium rate, whenever the surplus up-crosses the level b. The dividends are paid until the surplus down-crosses the level a, a < b . We assume that the claim sizes are phase-type distributed. In the analysis we apply the multidimensional Wald martingale, and the multidimensional Asmussesn and Kella martingale.

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.

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