Joint Survival Probability Research Articles

A Markov regime switching jump-diffusion model for the pricing of portfolio credit derivatives

The class of reduced form models is a very important class of credit risk models, and the modeling of the default dependence structure is essential in the reduced form models. This paper proposes a thinning-dependent structure model in the reduced form framework. The intensity process is the jump-diffusion version of the Vasicek model with the coefficients allowed to switch in different regimes. This article will investigate the joint (conditional) survival probability and the pricing formulas of portfolio credit derivatives. The exact analytical expressions are provided.

Optimal Reciprocal Reinsurance Treaties Under the Joint Survival Probability and the Joint Profitable Probability

AbstractA reinsurance treaty involves two parties, an insurer and a reinsurer. The two parties have conflicting interests. Most existing optimal reinsurance treaties only consider the interest of one party. In this article, we consider the interests of both insurers and reinsurers and study the joint survival and profitable probabilities of insurers and reinsurers. We design the optimal reinsurance contracts that maximize the joint survival probability and the joint profitable probability. We first establish sufficient and necessary conditions for the existence of the optimal reinsurance retentions for the quota‐share reinsurance and the stop‐loss reinsurance under expected value reinsurance premium principle. We then derive sufficient conditions for the existence of the optimal reinsurance treaties in a wide class of reinsurance policies and under a general reinsurance premium principle. These conditions enable one to design optimal reinsurance contracts in different forms and under different premium principles. As applications, we design an optimal reinsurance contract in the form of a quota‐share reinsurance under the variance principle and an optimal reinsurance treaty in the form of a limited stop‐loss reinsurance under the expected value principle.

Correlated intensity, counter party risks, and dependent mortalities

In this paper we use an intensity-based framework to analyze and compute the correlated default probabilities, both in finance and actuarial sciences, following the idea of “change of measure” initiated by Collin-Dufresne et al. (2004). Our method is based on a representation theorem for joint survival probability among an arbitrary number of defaults, which works particularly effectively for certain types of correlated default models, including the counter-party risk models of Jarrow and Yu (2001) and related problems such as the phenomenon of “flight to quality”. The results are also useful in studying the recently observed dependent mortality for married couples involving spousal bereavement. In particular we study in details a problem of pricing Universal Variable Life (UVL) insurance products. The explicit formulae for the joint-life status and last-survivor status (or equivalently, the probability distribution of first-to-default and last-to-default in a multi-firm setting) enable us to derive the explicit solution to the indifference pricing formula without using any advanced results in partial differential equations.

Assessing Economic Damages in Personal Injury and Wrongful Death Litigation: The State of Illinois

Forensic economics experts (FE) working with attorneys engaged in litigation, whether consulting, preparing a report, or testifying at deposition or trial, generally are expected to have some knowledge (1) of the state’s statutory and case law regarding allowable damages and methods; and (2) that certain topics (e.g., taxes, collateral sources) should not be mentioned or considered at certain times since a mistrial could result. This situation creates a tension: forensic economics experts are economics experts and are not attorneys, but nonetheless must have a reasonable understanding of the relevant state law. In this vein, the Journal of Forensic Economics (JFE) continues to publish a series of articles on the ways such damages are calculated in different state jurisdictions, one state at a time.2 The state of South Dakota is included in this issue and this paper adds Illinois to the list. Following the format of previous articles in this JFE series, Section II provides a listing of the controlling statutes, general case law, and court rules. Section III discusses the concept of earning capacity which appears throughout PI and WD case law in Illinois. Section IV discusses discounting to present value. Fringe benefits are discussed in Section V, while Section

Tail asymptotic results for elliptical distributions

Let ( X , Y ) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P { X > x , Y > y } and the conditional probability P { Y > y | X > x } , for x , y large.

Research Note: Assessing Household Service Losses with Joint Survival Probabilities

Traditional analyses of household service losses in personal injury and wrongful death litigation calculate the losses over the expected lifetime of the injured or deceased individual. In fact, the losses to the surviving family members are more accurately described by using joint survival probabilities of the injured or deceased person and their survivors, or a “joint life expectancy.” The use of joint probabilities will always serve to reduce expected household service losses and these reductions can be especially significant when the deceased is significantly younger than the surviving spouse or if the survivor has a relatively low remaining life expectancy. (This abstract was borrowed from another version of this item.)

Excess of loss reinsurance under joint survival optimality

Explicit expressions for the probability of joint survival up to time x of the cedent and the reinsurer, under an excess of loss reinsurance contract with a limiting and a retention level are obtained, under the reasonably general assumptions of any non-decreasing premium income function, Poisson claim arrivals and continuous claim amounts, modelled by any joint distribution. By stating appropriate optimality problems, we show that these results can be used to set the limiting and the retention levels in an optimal way with respect to the probability of joint survival. Alternatively, for fixed retention and limiting levels, the results yield an optimal split of the total premium income between the two parties in the excess of loss contract. This methodology is illustrated numerically on several examples of independent and dependent claim severities. The latter are modelled by a copula function. The effect of varying its dependence parameter and the marginals, on the solutions of the optimality problems and the joint survival probability, has also been explored.

Correlated Random Walks and the Joint Survival Probability

First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations are small, i.e., of order a few percent, but nonetheless including correlations is very important for managing portfolio credit risk and pricing some credit derivatives (e.g. first to default baskets). In first passage models the exact dependence of the joint survival probability of more than two firms on their asset correlations is not known. We derive an expression for the dependence of the joint survival probability of n firms on their asset correlations using first order perturbation theory in the correlations. It includes all terms that are linear in the correlations but neglects effects of quadratic and higher order. For constant time independent correlations we compare the first passage model expression for the joint survival probability with what a multivariate normal Copula function gives. As a practical application of our results we calculate the dependence of the five year joint survival probability for five basic industrials on their asset correlations.

Credit Events and the Valuation of Credit Derivatives of Basket Type

Thispaper provides a simple model for valuing a credit derivativewhose payoff depends on the identity (or identities) of the first(or first two) to occur of a given list of credit events, suchas defaults. The joint survival probability of occurrence timesof credit events is formulated in terms of stochastic intensityprocesses under the assumption of conditional independence. Basedon the joint survival probability, we can easily obtain the pricingformulas of such credit derivatives under the risk-neutral valuationframework. When the default intensity processes follow the extendedVasicek model, closed-form solutions of the pricing formulasare given.

Valuation of a Credit Swap of the Basket Type

This article provides a simple model to value a credit swap ofthe basket type. Unlike the previous literature, we considerthe joint survival probability of occurrence times of creditevents in terms of stochastic intensity processes under the assumptionof conditional independence. Based on the joint survival probability,such a credit swap can be valued under the risk-neutral valuationframework. Assuming that the default intensity processes followthe extended Vasicek model with a correlation structure, an analyticexpression of the valuation formula is derived. Some numericalexample is given to demonstrate the usefulness of our model.

A Multinomial Likelihood Model for Estimating Survival Probabilities and Overwintering for Fall Chinook Salmon Using Release: Recapture Methods

Standard release-recapture analysis, using Cormack-Jolly-Seber (CJS) models to estimate survival probabilities between hydroelectric facilities for juvenile Snake River fall chinook salmon (Oncorhynchus tschawytscha), ignore the possibility of individual fish overwintering and completing their migration in the year following tagging. These models do not utilize available capture history data from this second year and produce negatively biased estimates of survival probabilities. A new multinomial likelihood model was developed that results in biologically relevant, unbiased estimates of joint survival and overwintering probabilities using the full two years of capture history data. This model was applied to 1995 Snake River fall chinook hatchery releases to estimate the survival probability between a release site at Asotin, Washington (U.S.) and Lower Granite Dam. In the example presented here, overwintering is not a common physiological response and thus the use of CJS models (estimate of the survival probability = .4235; SE = .0162) did not result in an appreciably lower estimate for the survival probability than that calculated considering overwintering (estimate of the survival probability = .4360; SE = .0164) and obtained using the new multinomial model. However, analysis of releases in subsequent years may show greater impacts of overwintering on the estimates of survival probabilities.

Bounds on Reliability of a Coherent System with Positively Correlated Components

An upper bound on the reliability of a coherent system of positively correlated components is obtained via an improved Bonferroni inequality. An example is given. The bound is sharper if the joint survival probability is known for each pair of components.