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The Valuation of Options for Alternative Stochastic Processes
 Journal of Financial Economics
, 1976
"... This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have nol been used in previous models. The technique is applied lo these processes to find explicit option valuation formulas, ..."
Abstract

Cited by 679 (5 self)
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This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have nol been used in previous models. The technique is applied lo these processes to find explicit option valuation formulas
A subordinated stochastic process model with finite variance for speculative prices
 Econometrica
, 1973
"... Thanks are due to Hendrik Houthakker and Christopher Sims, for both encouragement and advice in developing this paper. As usual, all remaining errors are my own. This research was supported by a Harvard Dissertation Fellowship, NSF grant 33708, and the ..."
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Cited by 561 (1 self)
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Thanks are due to Hendrik Houthakker and Christopher Sims, for both encouragement and advice in developing this paper. As usual, all remaining errors are my own. This research was supported by a Harvard Dissertation Fellowship, NSF grant 33708, and the
Combinatorial stochastic processes
"... This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters ’ and numb ..."
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Cited by 228 (15 self)
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This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters
Tractable inference for complex stochastic processes
 In Proc. UAI
, 1998
"... The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a gi ..."
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Cited by 302 (14 self)
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The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a
◮...Stochastic Processes
"... ◮ A stochastic process is a family of random variables X(t), t ∈ T indexed by a parameter t in an index set T ◮ We will consider discretetime stochastic processes where T = Z (the integers) ◮ A time series is said to be strictly stationary if the joint distribution of X(t1),..., X(tn) is the same a ..."
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Cited by 2 (0 self)
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◮ A stochastic process is a family of random variables X(t), t ∈ T indexed by a parameter t in an index set T ◮ We will consider discretetime stochastic processes where T = Z (the integers) ◮ A time series is said to be strictly stationary if the joint distribution of X(t1),..., X(tn) is the same
STOCHASTIC PROCESSES
"... The course Stochastic Processes aims at showing the importance of stochastic models in which time plays a major role. The emphasis is on Markov decision processes. The models arise in many phenomena and have wide applications in operations, finance, marketing, economics, etc. Understanding the dynam ..."
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The course Stochastic Processes aims at showing the importance of stochastic models in which time plays a major role. The emphasis is on Markov decision processes. The models arise in many phenomena and have wide applications in operations, finance, marketing, economics, etc. Understanding
GENERALIZED STOCHASTIC PROCESSES by
"... generalized stochastic processes, information theory, sampling. ..."
Stochastic Processes
"... In this section we recall the basic vocabulary and results of probability theory. A probability space associated with a random experiment is a triple (Ω, F, P) where: (i) Ω is the set of all possible outcomes of the random experiment, and it is called the sample space. (ii) F is a family of subsets ..."
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In this section we recall the basic vocabulary and results of probability theory. A probability space associated with a random experiment is a triple (Ω, F, P) where: (i) Ω is the set of all possible outcomes of the random experiment, and it is called the sample space. (ii) F is a family of subsets of Ω which has the structure of a σfield: a) ∅ ∈ F b) If A ∈ F, then its complement A c also belongs to F c) A1, A2,... ∈ F = ⇒ ∪ ∞ i=1Ai ∈ F (iii) P is a function which associates a number P (A) to each set A ∈ F with the following properties: a) 0 ≤ P (A) ≤ 1, b) P (Ω) = 1 c) For any sequence A1, A2,... of disjoints sets in F (that is, Ai ∩ Aj = ∅ if i = j), P (∪ ∞ i=1Ai) = ∑∞ i=1 P (Ai) The elements of the σfield F are called events and the mapping P is called a probability measure. In this way we have the following interpretation of this model: P (F)=“probability that the event F occurs” The set ∅ is called the empty event and it has probability zero. Indeed, the additivity property (iii,c) implies P (∅) + P (∅) + · · · = P (∅). The set Ω is also called the certain set and by property (iii,b) it has probability one. Usually, there will be other events A ⊂ Ω such that P (A) = 1. If a statement holds for all ω in a set A with P (A) = 1, then it is customary to say that the statement is true almost surely, or that the statement holds for almost all ω ∈ Ω. The axioms a), b) and c) lead to the following basic rules of the probability calculus:
Results 1  10
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20,437