An Optimization Approach for Pricing of Sherpa Target Redemption Notes

Based on the one-factor CIR interest rate model, the pricing of Sherpa Target Redemption Notes (STARN) with early-excise features is investigated in this paper. Firstly, the characteristics of Sherpa target redemption notes were described and the partial differential equation was proposed. Secondly, both non-arbitrage jump conditions on the coupon date and early-excise policy on the redemption date were provided; furthermore, the boundary conditions of partial differential equations were also discussed. Thirdly, a numerical method for solving the partial differential equation was obtained based on the control volume in the theory of finite volume by making use of the upwind weighting scheme to avoid the numerical oscillation phenomenon. Finally, the sensitivity of the model parameters was analyzed. The results show that the STARN value decreases rapidly with the increase in short-term interest rates, furthermore, when short-term interest rates reached a turning point the rate of decline slowed. As volatility increases, the value of the Notes is increased; increasingly as the proportion redeemed is large, STARN value increases

Pricing and warranty decisions in a two-period closed loop supply chain

For a two-period closed loop supply chain (CLSC) consisting of a manufacturer and a retailer, Stackelberg game analyses are conducted to examine pricing and warranty decisions under two warranty models depending on who offers warranty for new and remanufactured products and the corresponding benchmark models with warranty for new products only. Next, we identify the conditions under which warranty for remanufactured products is offered and investigate how this warranty affects the CLSC operations. Subsequently, comparative studies are carried out to examine equilibrium decisions, profitability and consumer surplus of the CLSC between the two warranty models. Analytical results show that offering warranty for remanufactured products does not affect new product pricing in period 2, but influences pricing of new products in period 1 and remanufactured products in period 2, thereby enhancing remanufacturing, individual and channel profitability, and consumer surplus. Compared to the retailer warranty for remanufactured products, the manufacturer warranty can attain a more equitable profit distribution. If the warranty cost advantage of the manufacturer (retailer) is significant relative to that of the retailer (the manufacturer), the manufacturer (retailer) arises as a natural choice to offer warranty for remanufactured products as this decision enhances both profitability and consumer surplus

A Lévy Option Pricing model of FFT-Based High-order Multinomial Tree

This paper studies the method of constructing high order recombined multinomial tree based on fast Fourier transform (FFT), and applies multinomial tree option pricing under the Lévy process. First, the Lévy option pricing model and Fourier transform are introduced. Then, the network model based on FFT (Markov chain) is presented. After that, a method of constructing a recombined multinomial tree based on FFT is given. It is proved that the discrete random variables corresponding to the multinomial tree converge to the Lévy distributed continuous random variable. Next, we obtain the European option pricing formula of FFT multinomial tree pricing, and apply the reverse iteration method to the American option pricing. Finally, under the Jump-diffuse process, the difference between the computational accuracy and computational efficiency of the Semi-analytical solution of European Option and Merton European Call Option which are priced under FFT is compared. The results show that the method of constructing a high-order recombined multinomial tree based on FFT has very high calculation precision and calculation speed, which can solve the problem of traditional risk-neutral multinomial tree construction and it is a promising pricing method for derivative products

De-wetting of evaporating drops on regular patterns of triangular posts

Directional wicking and spreading of liquids can be achieved by regular micro-patterns of specifically designed topographic features that break the reflection symmetry of the underlying pattern. The present study aims to understand the formation and stability of wetting films during the evaporation of volatile liquid drops on surfaces with a micro-pattern of triangular posts arranged in a rectangular lattice. Depending on the density and aspect ratio of the posts, we observe either spherical-cap shaped drops with a mobile three-phase contact line or the formation of circular or angular drops with a pinned three-phase contact line. Drops of the latter class eventually evolve into a liquid film extending to the initial footprint of the drop and a shrinking cap-shaped drop sitting on the film. The drop evolution is controlled by the density and aspect ratio of the posts, while no influence of the orientation of the triangular posts on the contact line mobility becomes evident. Our experiments corroborate previous results of systematic numerical energy minimization, predicting that conditions for a spontaneous retraction of a wicking liquid film depend weakly on the orientation of the film edge relative to the micro-pattern

Improving Multi-turn Emotional Support Dialogue Generation with Lookahead Strategy Planning

Providing Emotional Support (ES) to soothe people in emotional distress is an essential capability in social interactions. Most existing researches on building ES conversation systems only considered single-turn interactions with users, which was over-simplified. In comparison, multi-turn ES conversation systems can provide ES more effectively, but face several new technical challenges, including: (1) how to adopt appropriate support strategies to achieve the long-term dialogue goal of comforting the user's emotion; (2) how to dynamically model the user's state. In this paper, we propose a novel system MultiESC to address these issues. For strategy planning, drawing inspiration from the A* search algorithm, we propose lookahead heuristics to estimate the future user feedback after using particular strategies, which helps to select strategies that can lead to the best long-term effects. For user state modeling, MultiESC focuses on capturing users' subtle emotional expressions and understanding their emotion causes. Extensive experiments show that MultiESC significantly outperforms competitive baselines in both dialogue generation and strategy planning. Our codes are available at https://github.com/lwgkzl/MultiESC.Comment: Accepted by the main conference of EMNLP 202