Martingales

Abstract. Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the class of simple trading strategies. This result can be seen as a generalization of a similar result on three dimensional Bessel process in [3]. We also provide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.

show abstract

“…Let X be the Bessel process of dimension δ ∈ (2, ∞) (see [12] Definition 11.1.1) and X 0 > 0. Then X satisfies the no arbitrage property in S(F).…”

Section: Example 2 Consider the Cev Modelmentioning

confidence: 99%

“…The process M t = X 2−δ is a nonnegative local martingale (see [12] Chapter 11, Exercise 1.16) and a regular strong Markov process. By Proposition 2 of [1] M has the sticky property and so it satisfies the condition (⋆).…”

Section: Example 2 Consider the Cev Modelmentioning

confidence: 99%

No arbitrage conditions for simple trading strategies

Bayraktar

Sayit

2009

Ann Finance

View full text Add to dashboard Cite

show abstract

“…More specifically, first it is well-known, cf. [25,§VI.2 and §XII.2], that the excursion lengths of a Brownian motion in [0,1] are the jumps of the inverse τ s := inf{t : T t > s} of the local time process T t in the interval 0 ≤ s ≥ T 1 , that τ s is a stable subordinator of index 1/2, and that the sizes of the jumps of τ s for 0 ≤ s ≤ a are given by a Poisson process on (0, ∞) with intensity a/ √ 2πx 3 . The equivalence of (i), (iii) and (v) now follows easily, cf.…”

Section: Unsuccessful Searchmentioning

confidence: 99%

Asymptotic distribution for the cost of linear probing hashing

Janson

2001

Random Struct Algorithms

View full text Add to dashboard Cite

show abstract

“…where w(t), t ≥ 0 is a standard three-dimensional Brownian motion, x ∈ R is identified with (x, 0, 0) ∈ R 3 and E stands for expectation, see [23], p. 251. The operator A 1 given by A 1 f = Af − f, f ∈ C[0, 1] appears implicitly in the recent model of kinase activity in a living cell [17].…”

Section: A Bessel Process With Mass Inflowmentioning

confidence: 99%

Lord Kelvin’s method of images in semigroup theory

Bobrowski

2010

Semigroup Forum

View full text Add to dashboard Cite

We show that Lord Kelvin's method of images is a way to prove generation theorems for semigroups of operators. To this end we exhibit three examples: a more direct semigroup-theoretic treatment of abstract delay differential equations, a new derivation of the form of the McKendrick semigroup, and a generation theorem The general ideaLord Kelvin's method of images is an ingenious way of solving problems involving boundary conditions, see e.g. [4,7,11,14,18,19,24] and references given there. The idea of employing the method to prove generation theorems for semigroups of operators goes apparently back to W. Feller who constructed the semigroup of the minimal (and the reflected) Brownian motion on R + by noting that the space of odd (even) functions is left invariant by the semigroup of the unrestricted Brownian motion on R, see [12], pp. 341-343, comp. [3]. These semigroups are generated by the one-dimensional Laplacian with Dirichlet and Neumann boundary conditions at the origin, respectively. A question whether a similar construction can be carried out also in the case of more general boundary conditions, seems to have been opened for Communicated

show abstract

Martingales

Cited by 140 publications

References 6 publications

No arbitrage conditions for simple trading strategies

No arbitrage conditions for simple trading strategies

Asymptotic distribution for the cost of linear probing hashing

Lord Kelvin’s method of images in semigroup theory

Contact Info

Product

Resources

About