A Numerical Method for a Continuous-Time Insurance-Consumption-Investment Model

2009 ◽  
Author(s):  
Jinchun Ye
Keyword(s):  
Numerical Method ◽  
Continuous Time ◽  
Investment Model ◽  
Insurance Consumption

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

scholarly journals Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 435
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Linear Programming ◽  
Robust Optimization ◽  
Numerical Method ◽  
Programming Problem ◽  
Continuous Time ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Robust Counterpart ◽  
Linear Programming Problems ◽  
Time Linear

A robust continuous-time linear programming problem is formulated and solved numerically in this paper. The data occurring in the continuous-time linear programming problem are assumed to be uncertain. In this paper, the uncertainty is treated by following the concept of robust optimization, which has been extensively studied recently. We introduce the robust counterpart of the continuous-time linear programming problem. In order to solve this robust counterpart, a discretization problem is formulated and solved to obtain the ϵ -optimal solution. The important contribution of this paper is to locate the error bound between the optimal solution and ϵ -optimal solution.

Insurance, Consumption, and Saving: A Dynamic Analysis in Continuous Time

2004 ◽  
Vol 94 (4) ◽  
pp. 1130-1140 ◽  
Author(s):  
R. A Somerville
Keyword(s):  
Life Insurance ◽  
Continuous Time ◽  
Precautionary Saving ◽  
Loss Probability ◽  
Optimal Consumption ◽  
The Maximum Principle ◽  
Consumption Decisions ◽  
Consumption And Saving ◽  
Insurance Consumption ◽  
Full Insurance

This paper shows how the demand for non-life insurance interacts with consumption and saving. The analysis is set in continuous time, using the maximum principle. When insurance is actuarially fair, the insurance and consumption decisions are separable. With loaded premiums, and alternatively without insurance, optimal consumption is dynamically related to the growth rate of the loss probability, and a growing loss probability generates precautionary saving. With loaded premiums, less than full insurance is demanded at each instant, and optimal cover varies over time, whether or not the loss probability is constant.

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