scholarly journals Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments

2004 ◽  
Vol 36 (4) ◽  
pp. 1278-1299 ◽  
Author(s):  
Qihe Tang ◽  
Gurami Tsitsiashvili
Keyword(s):  
Discrete Time ◽  
Time Horizon ◽  
Economic Environment ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Infinite Time ◽  
Time Period ◽  
Stochastic Returns ◽  
Regularly Varying

This paper investigates the finite- and infinite-time ruin probabilities in a discrete-time stochastic economic environment. Under the assumption that the insurance risk - the total net loss within one time period - is extended-regularly-varying or rapidly-varying tailed, various precise estimates for the ruin probabilities are derived. In particular, some estimates obtained are uniform with respect to the time horizon, and so apply in the case of infinite-time ruin.

scholarly journals Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments

2004 ◽  
Vol 36 (04) ◽  
pp. 1278-1299 ◽  
Author(s):  
Qihe Tang ◽  
Gurami Tsitsiashvili
Keyword(s):  
Discrete Time ◽  
Time Horizon ◽  
Economic Environment ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Infinite Time ◽  
Time Period ◽  
Stochastic Returns ◽  
Regularly Varying

This paper investigates the finite- and infinite-time ruin probabilities in a discrete-time stochastic economic environment. Under the assumption that the insurance risk - the total net loss within one time period - is extended-regularly-varying or rapidly-varying tailed, various precise estimates for the ruin probabilities are derived. In particular, some estimates obtained are uniform with respect to the time horizon, and so apply in the case of infinite-time ruin.

scholarly journals Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Yang Yang ◽  
Xinzhi Wang ◽  
Xiaonan Su ◽  
Aili Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Risk Model ◽  
Dependence Structure ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Main Claim ◽  
Regularly Varying ◽  
Heavy Tailed ◽  
Insurance Risk Model

This paper considers a by-claim risk model under the asymptotical independence or asymptotical dependence structure between each main claim and its by-claim. In the presence of heavy-tailed main claims and by-claims, we derive some asymptotic behavior for ruin probabilities.

scholarly journals Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Shaowei Zhou ◽  
Weihai Zhang
Keyword(s):  
Semidefinite Programming ◽  
Riccati Equation ◽  
Discrete Time ◽  
Time Horizon ◽  
Stochastic Systems ◽  
Positive Semidefinite ◽  
Algebraic Riccati Equation ◽  
Infinite Time ◽  
Lq Problem ◽  
Lq Control

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems. Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.

scholarly journals Power estimates for ruin probabilities

2005 ◽  
Vol 37 (03) ◽  
pp. 726-742 ◽  
Author(s):  
Harri Nyrhinen
Keyword(s):  
Time Horizon ◽  
Heavy Tails ◽  
Random Variables ◽  
Partial Sums ◽  
Ruin Probabilities ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Time Of Ruin ◽  
The Time Of Ruin ◽  
Crude Estimate

Let X 1, X 2,… be real-valued random variables. For u>0, define the time of ruin T = T(u) by T = inf{n: X 1+⋯+X n >u} or T=∞ if X 1+⋯+X n ≤u for every n = 1,2,…. We are interested in the ruin probabilities of general processes {X n } for large u. In the presence of heavy tails, one often finds power estimates. Our objective is to specify the associated powers and provide the crude estimate P(T≤xu)≈u −R(x) for large u, for a given x∈ℝ. The rate R(x) will be described by means of tails of partial sums and maxima of {X n }. We also extend our results to the case of the infinite time horizon.

ASYMPTOTIC RUIN PROBABILITIES IN FINITE HORIZON WITH SUBEXPONENTIAL LOSSES AND ASSOCIATED DISCOUNT FACTORS

2005 ◽  
Vol 20 (1) ◽  
pp. 103-113 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Stochastic Processes ◽  
Discrete Time ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Finite Time Ruin Probability ◽  
Discount Factors ◽  
Subexponential Class

Consider a discrete-time insurance risk model with risky investments. Under the assumption that the loss distribution belongs to a certain subclass of the subexponential class, Tang and Tsitsiashvili (Stochastic Processes and Their Applications 108(2): 299–325 (2003)) established a precise estimate for the finite time ruin probability. This article extends the result both to the whole subexponential class and to a nonstandard case with associated discount factors.

Optimal admission control for a single-server loss queue

2004 ◽  
Vol 41 (02) ◽  
pp. 535-546 ◽  
Author(s):  
Kyle Y. Lin ◽  
Sheldon M. Ross
Keyword(s):  
Admission Control ◽  
Time Horizon ◽  
Queueing System ◽  
Single Server ◽  
Sufficient Condition ◽  
Infinite Time ◽  
Discounted Cost ◽  
Time Period ◽  
Service Distribution ◽  
General Service

This paper presents a single-server loss queueing system where customers arrive according to a Poisson process. Upon arrival, the customer presents itself to a gatekeeper who has to decide whether to admit the customer into the system without knowing the busy–idle status of the server. There is a cost if the gatekeeper blocks a customer, and a larger cost if an admitted customer finds the server busy and therefore has to leave the system. The goal of the gatekeeper is to minimize the total expected discounted cost on an infinite time horizon. In the case of an exponential service distribution, we show that a threshold-type policy—block for a time period following each admission and then admit the next customer—is optimal. For general service distributions, we show that a threshold-type policy need not be optimal; we then present a sufficient condition for the existence of an optimal threshold-type policy.

scholarly journals Finite- and Infinite-Time Ruin Probabilities with General Stochastic Investment Return Processes and Bivariate Upper Tail Independent and Heavy-Tailed Claims

2013 ◽  
Vol 45 (1) ◽  
pp. 241-273 ◽  
Author(s):  
Fenglong Guo ◽  
Dingcheng Wang
Keyword(s):  
Risk Model ◽  
Heston Model ◽  
Ruin Probabilities ◽  
Investment Risk ◽  
Insurance Risk ◽  
Infinite Time ◽  
Asymptotic Behaviors ◽  
Special Cases ◽  
Investment Returns ◽  
Heavy Tailed

In this paper we investigate the asymptotic behaviors of the finite- and infinite-time ruin probabilities for a Poisson risk model with stochastic investment returns which constitute a general adapted càdlàg process and heavy-tailed claim sizes which are bivariate upper tail independent. The results of this paper show that the asymptotic ruin probabilities are dominated by the extreme of insurance risk but not by that of investment risk. As applications of the results, we discuss four special cases when the investment returns are determined by a fractional Brownian motion, an integrated Vasicek model, an integrated Cox–Ingersoll–Ross model, and the Heston model.

scholarly journals Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shaowei Zhou ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
Time Horizon ◽  
Algebraic Riccati Equation ◽  
Mean Square ◽  
Infinite Time ◽  
Lq Problem ◽  
The Cost ◽  
And Control ◽  
Indefinite Stochastic Lq Control ◽  
Lq Control

This paper studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming (SDP) and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation (SARE), and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method.

Sign in / Sign up

Export Citation Format

Share Document