arXiv subjects

Chuancun Yin

Publications and source records attributed to Chuancun Yin.

47 records · Page 3Linked to original sources

arXiv2014

Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs

In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting capital. In the first problem, we consider the classical dividend problem without capital injections. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of capital injections over strategies with positive surplus at all times. The third problem has the same objective as the second one, but without the constraints on capital injections. Under the assumption of proportional transaction costs, we identify the value function and the optimal strategies for any distribution of gains.

q-fin.PM↗

arXiv2014

The first passage time problem for mixed-exponential jump processes with applications in insurance and finance

This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps.

q-fin.CP↗

arXiv2014

Convexity of ruin probability and optimal dividend strategies for a general Levy process

In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we appeal to very recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.

math.PR↗

arXiv2014

On the optimal dividend problem for a spectrally positive Levy process

In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Levy process. This model including the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

q-fin.PM↗

arXiv2014

Optimal dividend problem for a generalized compound Poisson risk model

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model including the classical risk model and the Polya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy.

q-fin.PR↗

arXiv2014

Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. Kyprianou, Loeffen and Perez [28] have shown that a refraction strategy (also called threshold strategy) forms an optimal strategy under the condition that the Levy measure has a completely monotone density. In this paper, we propose an alternative approach to this optimal problem.

q-fin.PR↗

arXiv2014

Exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory

We consider the spectrally negative Levy processes and determine the joint laws for the quantities such as the first and last passage times over a fixed level, the overshoots and undershoots at first passage, the minimum, the maximum and the duration of negative values. We apply our results to insurance risk theory to find an explicit expression for the generalized expected discounted penalty function in terms of scale functions. Further, a new expression for the generalized Dickson's formula is provided.

math.PR↗

arXiv2013

An extension of Paulsen-Gjessing's risk model with stochastic return on investments

We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu functions as well as the expected discounted penalty functions at ruin caused by a claim or by oscillation; We also study the dividend problem for the threshold and barrier strategies, the moments and moment-generating function of the total discounted dividends until ruin are discussed. Some examples are given for special cases.

q-fin.CP↗

arXiv2013

Optimal dividends problem with a terminal value for spectrally positive Levy processes

In this paper we consider a modified version of the classical optimal dividends problem of de Finetti in which the dividend payments subject to a penalty at ruin. We assume that the risk process is modeled by a general spectrally positive Levy process before dividends are deducted. Using the fluctuation theory of spectrally positive Levy processes we give an explicit expression of the value function of a barrier strategy. Subsequently we show that a barrier strategy is the optimal strategy among all admissible ones. Our work is motivated by the recent work of Bayraktar, Kyprianou and Yamazaki (2013).

q-fin.PR↗

arXiv2011

Asymptotic results for tail probabilities of sums of dependent heavy-tailed random variables

Let $\{X_1, X_2, ... \}$ be a sequence of dependent heavy-tailed random variables with distributions $F_1, F_2,...$ on $(-\infty,\infty)$, and let $τ$ be a nonnegative integer-valued random variable independent of the sequence $\{X_k, k \ge 1\}$. In this framework, we study the asymptotic behavior of the tail probabilities of the quantities $X_{(n)} = \max_{1\le k \le n} X_k$, $S_n =\sum_{k=1}^n X_k$ and $S_{(n)}=\max_{1\le k\le n} S_k$ for $n>1$, and for those of their randomized versions $X_{(τ)}$, $S_τ$ and $S_{(τ)}$. We also consider applications of the results obtained to some commonly-used risk processes.

math.PR↗

arXiv2011

On optimality of the barrier strategy for a general Levy risk process

We consider the optimal dividend problem for the insurance risk process in a general Levy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Levy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. (2007) [Annals of Applied Probability 17, 156-180], Loeffen (2008) [Annals of Applied Probability 18, 1669-1680] and Kyprianou et al. (2010) [Journal of Theoretical Probability 23, 547-564] in which the same problem was considered under the spectrally negative Levy processes setting.

math.PR↗