Optimal Stopping of a Risk Reserve Process with Interest and Cost Rates

1998 ◽  
Vol 35 (1) ◽  
pp. 115-123 ◽  
Author(s):  
A. Schöttl
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Explicit Solution ◽  
Random Time ◽  
Insurance Company ◽  
Markov Modulated ◽  
Semimartingale Representation

The risk reserve process of an insurance company within a deteriorating Markov-modulated environment is considered. The company invests its capital with interest rate α; the premiums and claims are increasing with rates β and γ. The problem of stopping the process at a random time which maximizes the expected net gain in order to calculate new premiums is investigated. A semimartingale representation of the risk reserve process yields, under certain conditions, an explicit solution of the problem.

Optimal Stopping of a Risk Reserve Process with Interest and Cost Rates

1998 ◽  
Vol 35 (01) ◽  
pp. 115-123 ◽  
Author(s):  
A. Schöttl
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Explicit Solution ◽  
Random Time ◽  
Insurance Company ◽  
Markov Modulated ◽  
Semimartingale Representation

The risk reserve process of an insurance company within a deteriorating Markov-modulated environment is considered. The company invests its capital with interest rate α; the premiums and claims are increasing with rates β and γ. The problem of stopping the process at a random time which maximizes the expected net gain in order to calculate new premiums is investigated. A semimartingale representation of the risk reserve process yields, under certain conditions, an explicit solution of the problem.

scholarly journals The Optimal Strategy of Reinsurance-Investment Problem for an Insurer with Dynamic Income Under Stochastic Interest Rate

2016 ◽  
Vol 4 (3) ◽  
pp. 244-257
Author(s):  
Delei Sheng
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Control Technique ◽  
Stochastic Interest Rate ◽  
Insurance Company ◽  
Power Utility ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman ◽  
Constant Interest Rate

AbstractThis paper considers the reinsurance-investment problem for an insurer with dynamic income to balance the profit of insurance company and policy-holders. The insurer’s dynamic income is given by a net premium minus a dynamic reward budget item and the net premium is obtained according to the expected premium principle. Applying the stochastic control technique, a Hamilton-Jacobi-Bellman equation is established under stochastic interest rate model and the explicit solution is obtained by maximizing the insurer’s power utility of terminal wealth. In addition, the comparison with corresponding results under constant interest rate helps us to understand the role and influence of stochastic interest rates more in-depth.

Optimal stopping of a risk process: model with interest rates

2002 ◽  
Vol 39 (2) ◽  
pp. 261-270 ◽  
Author(s):  
Bogdan Krzysztof Muciek
Keyword(s):  
Interest Rates ◽  
Optimal Stopping ◽  
Process Model ◽  
Stopping Time ◽  
Risk Process ◽  
Risk Theory ◽  
Dynamic Programming Method ◽  
Insurance Company ◽  
Initial Capital ◽  
The Times

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a ≥ 0, receives premiums and pays out claims that occur according to a renewal process {N(t), t ≥ 0}. The times between consecutive claims are i.i.d. The sequence of successive claims is a sequence of i.i.d. random variables. The capital of the company is invested at interest rate α ∊ [0,1], claims increase at rate β ∊ [0,1]. The aim is to find the stopping time that maximizes the capital of the company. A dynamic programming method is used to find the optimal stopping time and to specify the expected capital at that time.

Optimal stopping of a risk process: model with interest rates

2002 ◽  
Vol 39 (02) ◽  
pp. 261-270 ◽  
Author(s):  
Bogdan Krzysztof Muciek
Keyword(s):  
Interest Rates ◽  
Optimal Stopping ◽  
Process Model ◽  
Stopping Time ◽  
Risk Process ◽  
Risk Theory ◽  
Dynamic Programming Method ◽  
Insurance Company ◽  
Initial Capital ◽  
The Times

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a ≥ 0, receives premiums and pays out claims that occur according to a renewal process {N(t), t ≥ 0}. The times between consecutive claims are i.i.d. The sequence of successive claims is a sequence of i.i.d. random variables. The capital of the company is invested at interest rate α ∊ [0,1], claims increase at rate β ∊ [0,1]. The aim is to find the stopping time that maximizes the capital of the company. A dynamic programming method is used to find the optimal stopping time and to specify the expected capital at that time.

scholarly journals A semi-Markov modulated interest rate model

2013 ◽  
Vol 83 (9) ◽  
pp. 2094-2102 ◽  
Author(s):  
Guglielmo D’Amico ◽  
Raimondo Manca ◽  
Giovanni Salvi
Keyword(s):  
Interest Rate ◽  
Rate Model ◽  
Interest Rate Model ◽  
Markov Modulated

scholarly journals An Optimal Stopping Problem for Jump Diffusion Logistic Population Model

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Yang Sun ◽  
Xiaohui Ai
Keyword(s):  
Optimal Stopping ◽  
Critical State ◽  
Explicit Solution ◽  
Population Model ◽  
Value Function ◽  
Jump Diffusion ◽  
Optimal Value Function ◽  
Optimal Stopping Problem ◽  
Optimal Value ◽  
Poisson Jump

This paper examines an optimal stopping problem for the stochastic (Wiener-Poisson) jump diffusion logistic population model. We present an explicit solution to an optimal stopping problem of the stochastic (Wiener-Poisson) jump diffusion logistic population model by applying the smooth pasting technique (Dayanik and Karatzas, 2003; Dixit, 1993). We formulate this as an optimal stopping problem of maximizing the expected reward. We express the critical state of the optimal stopping region and the optimal value function explicitly.

Some asymptotic results for optimal stopping based on capture times

1976 ◽  
Vol 13 (4) ◽  
pp. 741-750
Author(s):  
Robert L. Wardrop
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Linear Time ◽  
Random Time ◽  
Time Cost ◽  
Asymptotic Results ◽  
Expected Payoff

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Zi; where Z1, Z2, …, Zn are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.

Explicit solution of an optimal stopping problem: the burn-in of conditionally exponential components

1997 ◽  
Vol 34 (1) ◽  
pp. 267-282 ◽  
Author(s):  
C. Costantini ◽  
F. Spizzichino
Keyword(s):  
Markov Process ◽  
Statistical Model ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Explicit Solution ◽  
Prior Distribution ◽  
Unknown Parameter ◽  
Two Dimensional ◽  
Optimal Stopping Problem ◽  
Optimal Duration

We consider the problem of the optimal duration of a burn-in experiment for n identical units with conditionally exponential life-times of unknown parameter Λ. The problem is formulated as an optimal stopping problem for a suitably defined two-dimensional continuous-time Markov process. By exploiting monotonicity properties of the statistical model and of the costs we prove that the optimal stopping region is monotone (according to an appropriate definition) and derive a set of equations that uniquely determine it and that can be easily solved recursively. The optimal stopping region varies monotonically with the costs. For the class of problems corresponding to a prior distribution on Λ of type gamma it is shown how the optimal stopping region varies with respect to the prior distribution and with respect to n.

scholarly journals Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Guoan Huang ◽  
Guohe Deng ◽  
Lihong Huang
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Factor Model ◽  
Integral Representations ◽  
Quadrature Formulas ◽  
Short Term ◽  
Put Option ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Coupon Bond

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim's equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optimal stopping and exercise boundaries by quadrature formulas. Numerical results and discussions are provided.

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