Calibrated American option pricing by stochastic linear programming

Abstract

We propose an approach for computing the arbitrage-free interval for the price of an American option in discrete incomplete market models via linear programming. The main idea is built replicating strategies that use both the basic asset and some European derivatives available on the market for trading. This method goes under the name of calibrated option pricing and it has given significant results for European options. Here, we extend the analysis to American options showing that the arbitrage-free interval can be characterized in terms of martingale measures and that it gets significantly reduced with respect to the non-calibrated case.     

Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model

We consider a manufacturer who sells both the new and remanufactured versions of a product over its life cycle. The manufacturer’s profit depends crucially on her ability to synchronize product returns with the sales of the remanufactured product. This gives rise to a challenging dynamic optimization problem where the size of both the market and the user pool are dynamic and their current values depend on the entire history. We provide an analytical characterization of the manufacturer’s optimal pricing, production, and inventory policies which lead to a practical threshold policy with a small optimality gap. In addition, our analysis offers a number of interesting insights. First, the timing of remanufacturing activity and its co-occurrence with new product manufacturing critically depends on remanufacturing cost benefits, attractiveness of the remanufactured product and product return rate. Second, there is a small upward jump in the price of the new product when remanufacturing is introduced. Third, the manufacturer keeps the new product longer on the market as the cost of remanufacturing decreases. Fourth, partially satisfying demand for the remanufactured item is never optimal, i.e., it is satisfied either fully or not at all. Finally, user pool and inventory of returned products are substitutes in ensuring the supply for future remanufacturing.     

A numerical approach for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation

In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13 and we have the coefficients of Taylor expansion. In addition, numerical results are presented to demonstrate the effectiveness of the proposed method.     

Coupled coincidence point results on generalized distance in ordered cone metric spaces

In this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via $c$ -distance. We also proved some related coupled common fixed point theorems for such mappings. Our results generalize, extend, and unify several well-known comparable results in the literature regarding this topic. We present some examples to illustrate the concepts and results.     

Almost f-Cosymplectic Manifolds

The purpose of this paper is to study a new class of contact manifolds. Such manifolds are called almost f-cosymplectic manifolds. Several tensor conditions are studied for such type of manifolds. We conclude our results with two examples of almost f-cosymplectic manifolds.     

Distribution of eigenvalues for the discontinuous boundary-value problem with functional-manypoint conditions

In this study, we investigate the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also a point of discontinuity, a finite number of internal points and abstract linear functionals. So our problem is not a pure boundary-value one. We single out a class of linear functionals and find simple algebraic conditions on the coefficients which guarantee the existence of an infinite number of eigenvalues. Also, the asymptotic formulas for the eigenvalues are found. The results obtained in this paper are new, even in the case of boundary conditions either without internal points or without linear functionals.     

Two-sided linear split quaternionic equations with n unknowns

In this paper, we investigate linear split quaternionic equations with the terms of the form axb. We give a new method of solving general linear split quaternionic equations with one, two and n unknowns. Moreover, we present some examples to show how this procedure works.     

On polyhedral extension of some LP theorems

McLinden (Mathematical Programming 24 (1982) 162–176) has extended theorems of Tucker (1956) and Williams (1970) on the complementarity behaviour of feasible and optimal solutions to a pair of canonical linear programs to proper convex polyhedral functions. He achieved this by heavily using the well-developed machinery of convex analysis. In this note, we prove most of his results mainly using linear programming theory.