Pricing via anticipative stochastic calculus

1994 ◽  
Vol 26 (04) ◽  
pp. 1006-1021
Author(s):  
Eckhard Platen ◽  
Rolando Rebolledo
Keyword(s):  
Structural Properties ◽  
General Model ◽  
Stochastic Calculus ◽  
Stochastic Equations ◽  
Stochastic Integrals ◽  
Derivative Securities

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

Pricing via anticipative stochastic calculus

1994 ◽  
Vol 26 (4) ◽  
pp. 1006-1021
Author(s):  
Eckhard Platen ◽  
Rolando Rebolledo
Keyword(s):  
Structural Properties ◽  
General Model ◽  
Stochastic Calculus ◽  
Stochastic Equations ◽  
Stochastic Integrals ◽  
Derivative Securities

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

Some New Examples of Lie Super-Algebra Representations Arising from Quantum Stochastic Calculus

1998 ◽  
Vol 01 (01) ◽  
pp. 33-42
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Stochastic Calculus ◽  
Stochastic Integrals ◽  
Quantum Stochastic Calculus

Following the methods of Refs. 1 and 2 we construct here a family of Lie super-algebra representations in terms of quantum stochastic integrals.

scholarly journals On the Dynamics of Semimartingales with Two Reflecting Barriers

2013 ◽  
Vol 50 (3) ◽  
pp. 671-685 ◽  
Author(s):  
Mats Pihlsgård ◽  
Peter W. Glynn
Keyword(s):  
Structural Properties ◽  
Explicit Construction ◽  
General Relationship ◽  
Local Times ◽  
Stochastic Integrals ◽  
Reflecting Barriers ◽  
Additional Assumptions

We consider a semimartingale X which is reflected at an upper barrier T and a lower barrier S, where S and T are also semimartingales such that T is bounded away from S. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective barriers to X, S, and T. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions on X, S, and T, e.g. if we take X, S, and T to be independent martingales (which satisfy some extra technical conditions).

On the Dynamics of Semimartingales with Two Reflecting Barriers

2013 ◽  
Vol 50 (03) ◽  
pp. 671-685 ◽  
Author(s):  
Mats Pihlsgård ◽  
Peter W. Glynn
Keyword(s):  
Structural Properties ◽  
Explicit Construction ◽  
General Relationship ◽  
Local Times ◽  
Stochastic Integrals ◽  
Reflecting Barriers ◽  
Additional Assumptions

We consider a semimartingaleXwhich is reflected at an upper barrierTand a lower barrierS, whereSandTare also semimartingales such thatTis bounded away fromS. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective barriers toX,S, andT. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions onX,S, andT, e.g. if we takeX,S, andTto be independent martingales (which satisfy some extra technical conditions).

Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus

1998 ◽  
Vol 01 (03) ◽  
pp. 455-466 ◽  
Author(s):  
Zhiyuan Huang ◽  
Shunlong Luo
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Stochastic Analysis ◽  
Stochastic Calculus ◽  
Stochastic Integrals ◽  
Algebra Structure ◽  
Quantum Stochastic Calculus ◽  
Fundamental Properties ◽  
White Noise Calculus ◽  
Wick Calculus

A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated. As applications, quantum stochastic integrals and quantum stochastic differential equations are treated from the viewpoint of Wick calculus.

Stochastic integrals and stochastic equations in set-valued and fuzzy-valued frameworks

2019 ◽  
Vol 20 (01) ◽  
pp. 2050001
Author(s):  
Mariusz Michta
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Stochastic Integrals ◽  
Finite Variation

In this paper, we study the existence, uniqueness and properties of solutions to set-valued and fuzzy-valued stochastic differential equations with respect to finite variation and martingale integrators. We present new types of such equations that generalize those studied earlier. For this aim we introduce properly defined new types of stochastic integrals in set-valued and fuzzy-valued settings and we establish their main properties. The results obtained in the paper generalize conclusions dealing with this topic known both in deterministic and stochastic cases.

scholarly journals Stability and structural properties of stochastic storage networks

1996 ◽  
Vol 33 (04) ◽  
pp. 1169-1180 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Structural Properties ◽  
Stability Condition ◽  
General Model ◽  
Initial Conditions ◽  
Internal Flows ◽  
Stationary Increments ◽  
Fluid Network ◽  
Storage Networks ◽  
Stochastic Fluid

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with non-zero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

scholarly journals Stability and structural properties of stochastic storage networks

1996 ◽  
Vol 33 (4) ◽  
pp. 1169-1180 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Structural Properties ◽  
Stability Condition ◽  
General Model ◽  
Initial Conditions ◽  
Internal Flows ◽  
Stationary Increments ◽  
Fluid Network ◽  
Storage Networks ◽  
Stochastic Fluid

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with non-zero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

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