We introduce a variant of the classic sealed-bid unit-demand auction in which each item has an associated put option. The put option of an item is held by the seller of the item, and gives the holder the right to sell the item to a specified target bidder at a specified strike price, regardless of market conditions. Unexercised put options expire when the auction terminates. In keeping with the...

To solve a mathematical model for American put option with uncertainty, we utilize two essentials, i.e., a λ−weighting function and a mean value of fuzzy random variables simultaneously. Estimation of randomness and fuzziness as uncertainty should be important when we deal with a reasonable and natural model extended from the original optimization/decision making. Three kinds of mean values by ...

Though an analytical solution for the value of a European option in the context of the Black-Scholes model is more than 30 years old, a corresponding solution for American options has troubled practitioners and academics alike. In 2006, an analytical solution was presented for puts, however, this solution is computationally complex, requiring symbolic algebra packages, that make it impractical ...

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim’s equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optim...

In this paper, we discuss the Banach fixed point theorem conditions on optimal exercise boundary of American put option paying continuously dividend yield, to investigate whether its existence, uniqueness, and convergence are derived. respect, consider integral representation which is extracted as a consequence Feynman-Kac formula. order prove above features, define nonempty closed set in space...

In this paper, we use Mellin transform to get the expression for the free boundary an price of an American finite-lived option, when the underlying is govern by the Levy process. We have also derived the free boundary and price of an American perpetual put as the limit of the preceded finite-lived option. We then show how to compute the price of an American option on a basket of stocks using Me...

Since Black and Scholes published their seminal paper [2] in 1973, the pricing of options by means of deterministic partial differential equations or inequalities has become standard practise in computational finance. An option gives the right (but not the obligation) to buy (call option) or sell (put option) a share for a certain value (the exercise price K) at a certain time T (exercise date)...