Results 1  10
of
16
Numerical Valuation of High Dimensional Multivariate American Securities
, 1994
"... We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted ..."
Abstract

Cited by 96 (0 self)
 Add to MetaCart
We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted expected cash flows under the modified riskneutral information process. Several efficient numerical techniques exist for pricing American securities depending on one or few (up to 3) risk sources. They are either latticebased techniques or finite difference approximations of the BlackScholes diffusion equation. However, these methods cannot be used for highdimensional problems, since their memory requirement is exponential in the
Pricing of American PathDependent Contingent Claims
, 1994
"... We consider the problem of pricing pathdependent contingent claims. Classically, this problem can be cast into the BlackScholes valuation framework through inclusion of the pathdependent variables into the state space. This leads to solving a degenerate advectiondiffusion Partial Differential Eq ..."
Abstract

Cited by 39 (1 self)
 Add to MetaCart
We consider the problem of pricing pathdependent contingent claims. Classically, this problem can be cast into the BlackScholes valuation framework through inclusion of the pathdependent variables into the state space. This leads to solving a degenerate advectiondiffusion Partial Differential Equation (PDE). Standard Finite Difference (FD) methods are known to be inadequate for solving such degenerate PDE. Hence, pathdependent European claims are typically priced through MonteCarlo simulation. To date, there is no numerical method for pricing pathdependent American claims. We first establish necessary and sufficient conditions amenable to a Lie algebraic characterization, under which degenerate diffusions can be reduced to lowerdimensional nondegenerate diffusions on a submanifold of the underlying asset space. We apply these results to pathdependent options. Then, we describe a new numerical technique, called Forward Shooting Grid (FSG) method, that efficiently copes with de...
OrderSorted Feature Theory Unification
, 1997
"... Ordersorted feature (OSF) terms provide an adequate representation for objects as flexible records. They are sorted, attributed, possibly nested, structures, ordered thanks to a subsort ordering. Sort definitions offer the functionality of classes imposing structural constraints on objects. These c ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
Ordersorted feature (OSF) terms provide an adequate representation for objects as flexible records. They are sorted, attributed, possibly nested, structures, ordered thanks to a subsort ordering. Sort definitions offer the functionality of classes imposing structural constraints on objects. These constraints involve variable sorting and equations among feature paths, including selfreference. Formally, sort definitions may be seen as axioms forming an OSF theory. OSF theory unification is the process of normalizing an OSF term, using sortunfolding to enforce structural constraints imposed on sorts by their definitions. It allows objects to inherit, and thus abide by, constraints from their classes. A formal system is thus obtained that logically models record objects with recursive class definitions accommodating multiple inheritance. We show that OSF theory unification is undecidable in general. However, we propose a set of confluent normalization rules which is complete for detecti...
Functions as Passive Constraints in LIFE
 ACM Transactions on Programming Languages and Systems
, 1994
"... LIFE is an experimental programming language proposing to integrate logic programming, functional programming, and objectoriented programming. It replaces firstorder terms with ψterms, data structures which allow computing with partial information. These are approximation structures denoting se ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
LIFE is an experimental programming language proposing to integrate logic programming, functional programming, and objectoriented programming. It replaces firstorder terms with ψterms, data structures which allow computing with partial information. These are approximation structures denoting sets of values. LIFE further enriches the expressiveness of ψterms with functional dependency constraints. We must explain the meaning and use of functions in LIFE declaratively as solving partial information constraints. These constraints do not attempt to generate their solutions but behave as demons filtering out anything else.
The Typed Polymorphic LabelSelective λCalculus
 IN PROC. ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1994
"... Formal calculi of record structures have recently been a focus of active research. However, scarcely anyone has studied formally the dual notioni.e., argumentpassing to functions by keywords, and its harmonization with currying. We have. Recently, we introduced the labelselective calculus, a ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Formal calculi of record structures have recently been a focus of active research. However, scarcely anyone has studied formally the dual notioni.e., argumentpassing to functions by keywords, and its harmonization with currying. We have. Recently, we introduced the labelselective calculus, a conservative extension of calculus that uses a labeling of abstractions and applications to perform unordered currying. In other words, it enables some form of commutation between arguments. This improves program legibility, thanks to the presence of labels, and efficiency, thanks to argument commuting. In this paper, we propose a simply typed version of the calculus, then extend it to one with MLlike polymorphic types. For the latter calculus, we establish the existence of principal types and we give an algorithm to compute them. Thanks to the fact that labelselective calculus is a conservative extension of calculus by adding numeric labels to stand for argument positions, its...
LabelSelective ...Calculus
"... We introduce an extension of calculus, called labelselective calculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in ord ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We introduce an extension of calculus, called labelselective calculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in order to preserve currying. This extension of calculus is conservative in the sense that when the set of labels is the singleton f1g, it coincides with calculus. The main result of this paper is the proof that the labelselective calculus is confluent. In other words, argument selection and reduction commute. R esum e Nous presentons une extension du calcul, appelee calcul labelselectif, dans laquelle les arguments des fonctions sont selectionnes par des etiquettes. L'ensemble des etiquettes comprend des positions numeriques aussi bien que des motclefs symboliques. Alors que ces derniers jouissent d'une commutativite libre, les premiers obeissent a une precedence relative pour preserver...