scholarly journals Optimal consumption/portfolio choice with borrowing rate higher than deposit rate

1998 ◽  
Vol 39 (4) ◽  
pp. 449-462 ◽  
Author(s):  
Wensheng Xu ◽  
Shuping Chen
Keyword(s):  
Portfolio Choice ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Optimal Consumption ◽  
Bank Account ◽  
Normal Diffusion ◽  
Hamilton Jacobi Bellman ◽  
Log Normal ◽  
Optimal Consumption And Investment

AbstractIn this paper, optimal consumption and investment decisions are studied for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r(t) for any deposit, and vice takes at a larger rate r′(t) for any loan. Optimal strategies are obtained via Hamilton-Jacobi-Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, we get the optimal consumption and optimal investment explicitly, which coincides with the classical one under the condition r′(t) ≡ r(t)

scholarly journals Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 1012-1026
Author(s):  
Sahar Albosaily ◽  
Serguei Pergamenchtchikov
Keyword(s):  
Financial Markets ◽  
Numerical Simulations ◽  
Financial Market ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Dynamical Programming ◽  
Verification Theorem ◽  
Logarithmic Utility ◽  
Hamilton Jacobi Bellman ◽  
Optimal Investment And Consumption

We consider a spread financial market defined by the multidimensional Ornstein–Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions using a stochastic dynamical programming method. We show a special verification theorem for this case. We find the solution to the Hamilton–Jacobi–Bellman (HJB) equation in explicit form and as a consequence we construct optimal financial strategies. Moreover, we study the constructed strategies with numerical simulations.

scholarly journals Consumption and Portfolio Choice under Internal Multiplicative Habit Formation

2019 ◽  
Vol 55 (7) ◽  
pp. 2334-2371
Author(s):  
Servaas van Bilsen ◽  
A. Lans Bovenberg ◽  
Roger J. A. Laeven
Keyword(s):  
Portfolio Choice ◽  
Habit Formation ◽  
Optimal Consumption ◽  
Investment Behavior ◽  
Risky Assets ◽  
General Utility ◽  
Marginal Propensity To Consume ◽  
Investment Opportunities ◽  
Marginal Propensity ◽  
Optimal Consumption And Investment

This paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit. We obtain closed-form policies under general utility functionals and stochastic investment opportunities by developing a nontrivial linearization to the budget constraint. This enables us to explicitly characterize how habit formation affects the marginal propensity to consume and optimal stock–bond investments. We also show that in a setting that combines habit formation with Epstein–Zin utility, consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease.

scholarly journals An Application of Dynamic Programming Principle in Corporate International Optimal Investment and Consumption Choice Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Zongyuan Huang ◽  
Zhen Wu
Keyword(s):  
Dynamic Programming ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Bank Account ◽  
Optimal Investment Strategy ◽  
Lower Interest Rate ◽  
Optimal Investment And Consumption ◽  
Utility Problem

This paper is concerned with a kind of corporate international optimal portfolio and consumption choice problems, in which the investor can invest her or his wealth either in a domestic bond (bank account) or in an oversea real project with production. The bank pays a lower interest rate for deposit and takes a higher rate for any loan. First, we show that Bellman's dynamic programming principle still holds in our setting; second, in terms of the foregoing principle, we obtain the investor's optimal portfolio proportion for a general maximizing expected utility problem and give the corresponding economic analysis; third, for the special but nontrivial Constant Relative Risk Aversion (CRRA) case, we get the investors optimal investment and consumption solution; last but not least, we give some numerical simulation results to illustrate the influence of volatility parameters on the optimal investment strategy.

scholarly journals Optimal Portfolio of Corporate Investment and Consumption Problem under Market Closure: Inflation Case

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zongyuan Huang ◽  
Detao Zhang
Keyword(s):  
Optimal Strategy ◽  
Direct Method ◽  
Absolute Risk ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Market Opening ◽  
Hamilton Jacobi Bellman Equation ◽  
The Difference ◽  
Hamilton Jacobi Bellman ◽  
The Relationship

We present the model of corporate optimal investment with consideration of the influence of inflation and the difference between the market opening and market closure. In our model, the investor has three market activities of his or her choice: investment in project A, investment in project B, and consumption. The optimal strategy for the investor is obtained using the Hamilton-Jacobi-Bellman equation which is derived using the dynamic programming principle. Further along, a specific case, the Hyperbolic Absolute Risk Aversion case, is discussed in detail, where the explicit optimal strategy can be obtained using a very simple and direct method. At the very end, we present some simulation results along with a brief analysis of the relationship between the optimal strategy and other factors.

scholarly journals Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiaotao Liu ◽  
Hailong Liu
Keyword(s):  
Portfolio Choice ◽  
Optimal Investment ◽  
Risk Process ◽  
Cev Model ◽  
Constant Elasticity ◽  
Economic Implications ◽  
Constant Elasticity Of Variance ◽  
Surplus Process ◽  
Hamilton Jacobi Bellman ◽  
Negative Exponential

This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.

scholarly journals Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Xiangbo Meng ◽  
Ximin Rong ◽  
Lidong Zhang ◽  
Ziping Du
Keyword(s):  
Model Uncertainty ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Model Parameters ◽  
Case Scenario ◽  
Worst Case ◽  
New Business ◽  
Hamilton Jacobi Bellman ◽  
Quadratic Distance ◽  
The Impact

In this paper, we study optimal investment-reinsurance strategies for an insurer who faces model uncertainty. The insurer is allowed to acquire new business and invest into a financial market which consists of one risk-free asset and one risky asset whose price process is modeled by a Geometric Brownian motion. Minimizing the expected quadratic distance of the terminal wealth to a given benchmark under the “worst-case” scenario, we obtain the closed-form expressions of optimal strategies and the corresponding value function by solving the Hamilton-Jacobi-Bellman (HJB) equation. Numerical examples are presented to show the impact of model parameters on the optimal strategies.

scholarly journals Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Optimal Strategies ◽  
Proportional Reinsurance ◽  
Two Dimensional ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Poisson Risk Model

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.

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