we use the basic binomial option pricing method but allow someor all the parameters in the model to be uncertain and model this uncertaintyusing fuzzy numbers. we show that with the fuzzy model we can, with areasonably small number of steps, consider almost all possible future stockprices; whereas the crisp model can consider only n + 1 prices after n steps.

A binomial lattice based framework for the analysis of finite investment options with finite operational phase is developed. Solutions for European and American type finite horizon investment options with optimal capital structure and a multi-stage investment setting with multiple debt issues are discussed. The analysis shows that optimal leverage ratios are not affected by option moneyness at ...

Locational marginal pricing (LMP) is a widely employed method for pricing electricity in the wholesale electricity market. Although it is well known that the LMP mechanism is vulnerable to market manipulation, there is little literature providing a systematic analysis of this phenomenon. In the first part of this paper, we investigate the economic dispatch outcomes of the LMP mechanism with str...

In this paper, we present a non-commutative version of some portions of finance theory, including theory of arbitrage, asset princing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. The binomial model (or, the CRR-model) is studied in the non-commutative setting, and in particular, we prove that a single-step model in non-commutative sett...

In this paper, we discuss statistical families P with the property that if the distribution of a random variable X is in P, then so is the distribution of ZwBi(X, p) for 0%p%1. (Here we take ZwBi(X, p) to mean that given XZx, Z is a draw from the binomial distribution Bi(x, p).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probabilit...

Here we model the price of a stock in discrete time by a Markov chain of the recursive form Sn+1 = SnYn+1, n ≥ 0, where the {Yi} are iid with distribution P (Y = u) = p, P (Y = d) = 1 − p. Here 0 < d < 1 + r < u are constants with r the risk-free interest rate ((1 + r)x is the payoff you would receive one unit of time later if you bought $x worth of the risk-free asset (a bond for example, or p...

Financial derivatives are contracts concerning rights and obligations to engage in future transactions on some underlying financial instrument. A major concern in financial markets is to compute an expected value of such contracts as a basis for trading decisions. The Cox, Ross and Rubinstein (CRR) binomial tree model is a popular discrete approach to such computations, which requires time quad...

California’s history, landscape, and identity have been marked indelibly by its vast and sometimes controversial infrastructure. Over the last decade, however, the state has replenished and repaired that infrastructure at an annual rate of less than 1 percent. As a result, identified needs now exceed available resources. In response to this problem, the governor has charged the Commission on Bu...

We tested a social television system with both voice and text communication in the field for one week, in four households. Participants expressed a preference for the freeform communication features over an earlier system with restricted communication options. Use of the communication features was nevertheless sporadic. Text was used more often than voice communication. However, both were usual...

Large public screens are proliferating in public spaces. Today, most of them are standalone installations that display advertisements in the form of slides, short movies, or still images. However, it is not hard to imagine that these displays will soon be connected through the Internet, thus creating a global and powerful communication medium capable of providing rich, interactive applications....