This paper concerns with the pricing of American options by simulation methods. In the traditional methods, in order to determine when to exercise, we have to store the simulated asset prices at all time steps on all paths. If N time steps and M paths are used, then the storage requirement is O(MN). In this paper, we present a simulation method for pricing American options where the number of s...

One can prove the following propositions: (1) Let I be a set, f be a function, and F , G be many sorted functions indexed by I. If rng f ⊆ I, then (G ◦ F ) · f = (G · f) ◦ (F · f). (2) Let S be a non empty non void many sorted signature, o be an operation symbol of S, V be a non-empty many sorted set indexed by the carrier of S, and x be a set. Then x is an argument sequence of Sym(o, V ) if an...

We consider the problem of determining when a given source can be used to approximate the output due to any input to a given channel. We provide achievability and converse results for a general source and channel. For the special case of a full-rank discrete memoryless channel we give a stronger converse result than we can give for a general channel.

We consider a multiserver queueing system in which customers request service from a random number of identical servers. In contrast to batch arrival queues, customers cannot begin service until all required servers are available. Servers assigned to the same customer may free separately. For this model, we derive the steady-state distribution for waiting time, the distribution of busy servers, ...

Special orthogonal n × n matrices with rational elements form the group SO(n, Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for generating such matrices by means of random number routines.

For simplicity, we adopt the following rules: X denotes a non empty set, F denotes a sequence of partial functions from X into R with the same dom, s1, s2, s3 denote sequences of extended reals, x denotes an element of X, a, r denote extended real numbers, and n, m, k denote natural numbers. We now state several propositions: (1) If for every natural number n holds s2(n) ≤ s3(n), then inf rng s...

We show that the short period of the uniform random number generator in the published implementation of Marsaglia and Tsang’s Ziggurat method for generating random deviates can lead to poor distributions. Changing the uniform random number generator used in its implementation fixes this issue.

We consider the problem of deterministically selecting s uniformly random diierent m-element subsets of f1; :::; kg. The only known lower bound for the time to solve this problem is the trivial (sm). The best two previously known solutions are of time O(sm 3 log m log log m) and O(s(k + m)), respectivly. In this paper we present an algorithm whose time comlexity is O(s 2 m 2 + sm 2 log m log lo...