Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

The impact of dynamic pricing on the economic order decision

This paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer. Items are procured from an external supplier according to the economic order quantity (EOQ) model and are sold to customers on a single market without competition following the simple monopolist pricing problem. Coordinated decision making of optimal pricing and ordering is influenced by operating costs – including ordering and inventory holding costs – and the demand rate obtained from a price response function. The retailer is allowed to vary the selling price, either in a fixed number of discrete points in time or continuously. While constant and continuous pricing have received much attention in the literature, problems with a limited number of price changes are rather rare. This paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the EOQ model, that is to trigger high demand rates when inventories are high. We provide structural properties of the optimal time instants when the price should be changed. Taking into account costs for changes in price, it provides numerical guidance on number, timing, and size of price changes during an order cycle. Numerical examples show that the benefits of dynamic pricing in an EOQ framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing.     

Asset pricing for an affine jump‐diffusion model using an FD method of lines on nonuniform meshes

We present a novel numerical scheme for the valuation of options under a well‐known jump‐diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro‐differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments.     

Reinsurance contract design when the insurer is ambiguity-averse

This paper investigates proportional and excess-loss reinsurance contracts in a continuous-time principal–agent framework, in which the insurer is the agent and the reinsurer is the principal. Insurance claims follow the classic Cramér–Lundberg process. The insurer believes that the claim intensity is uncertain and he chooses robust risk retention levels to maximize the penalty-dependent multiple-priors utility. The reinsurer designs reinsurance contracts subject to the insurer’s incentive compatibility constraints. The analytical expressions of the two robust reinsurance contracts are derived. Our results show that the robust reinsurance demand and price are greater than their respective standard values without model ambiguity, and increase as the insurer’s ambiguity aversion increases. Moreover, the reinsurer specifies a decreasing reinsurance price to induce increasing demand over time. Specifically, the price of excess-loss reinsurance is higher, relative to that of proportional reinsurance. Further, only if the insurer’s risk aversion is high or the reinsurer’s risk aversion is low, the insurer prefers the excess-loss reinsurance contract.     

Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion

This paper considers the robust equilibrium reinsurance and investment strategies for an ambiguity-averse insurer under a dynamic mean–variance criterion. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of a risk-free asset and a credit default swap (CDS). Following a game theoretic approach, robust equilibrium strategies and equilibrium value functions for the pre-default case and the post-default case are derived, respectively. For the ambiguity-averse insurer, in general the equilibrium strategies can be characterized by unique solutions to some algebraic equations. For the degenerate case with an ambiguity-neutral insurer, closed-form expressions of equilibrium strategies and equilibrium value functions are obtained. Numerical examples demonstrate that the consideration of model uncertainty and CDS investment improves the insurer’s utility. In this regard, our paper establishes theoretical and numerical support for the importance of ambiguity aversion, credit risk and their interplay in insurance business.     

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.     

Stochastic model for market stocks with floors

We present a model to describe the stochastic evolution of stocks that show a strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The related problem of how to prize general securities that pay dividends at a continuous rate and earn a terminal payoff at maturity T is solved via the martingale probability approach.     

均衡信贷配给的期权定价分析

本文基于期权定价的视角分析信贷配给，以一条全新的思路阐释均衡信贷配给的成因及特征，并试图得出些许启示。     

Sensitivity Analysis Based Method for Optimal Road Network Pricing

Road pricing is an important economic measure for optimal management of transportation networks. The optimization objectives can be the total travel time or total cost incurred by all the travelers, or some other environmental objective such as minimum emission of dioxide, an so on. Suppose a certain toll is posed on some link on the network, this will give an impact on flows over the whole network and brings about a new equilibrium state. An equilibrium state is a state of traffic network at which no traveler could decrease the perceived travel cost by unilaterally changing the route. The aim of the toll setting is to achieve such an equilibrium state that a certain objective function is optimized. The problem can be formulated as a mathematical program with equilibrium constraints (MPEC). A key step for solving such a MPEC problem is the sensitivity analysis of traffic flows with respect to the change of link characteristics such as the toll prices. In this paper a sensitivity analysis based method is proposed for solving optimal road pricing problems.