The Experts below are selected from a list of 191604 Experts worldwide ranked by ideXlab platform
Ioane Muni Toke - One of the best experts on this subject based on the ideXlab platform.
-
stationary distribution of the volume at the best quote in a poisson order book model
International Journal of Theoretical and Applied Finance, 2017Co-Authors: Ioane Muni TokeAbstract:We develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using Applied Probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.
-
stationary distribution of the volume at the best quote in a poisson order book model
arXiv: Trading and Market Microstructure, 2015Co-Authors: Ioane Muni TokeAbstract:In this paper, we develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using Applied Probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.
Larry Shepp - One of the best experts on this subject based on the ideXlab platform.
-
on occupation times of the first and third quadrants for planar brownian motion
Journal of Applied Probability, 2017Co-Authors: Philip Ernst, Larry SheppAbstract:In Bingham and Doney (1988) the authors presented the Applied Probability community with a question which is very simply stated, yet is extremely difficult to solve: what is the distribution of the quadrant occupation time of planar Brownian motion? In this paper we study an alternate formulation of this long-standing open problem: let X ( t ), Y ( t ) t ≥0, be standard Brownian motions starting at x , y , respectively. Find the distribution of the total time T =Leb{ t ∈[0,1]: X ( t )× Y ( t )>0}, when x = y =0, i.e. the occupation time of the union of the first and third quadrants. If two adjacent quadrants are used, the problem becomes much easier and the distribution of T follows the arcsine law.
-
on occupation times of the first and third quadrants for planar brownian motion
arXiv: Probability, 2016Co-Authors: Philip Ernst, Larry SheppAbstract:An open problem of interest, first infused into the Applied Probability community in the work of Bingham and Doney in 1988, (see \cite{Bingham}) is stated as follows: find the distribution of the quadrant occupation time of planar Brownian motion. In this short communication, we study an alternate formulation of this longstanding open problem: let $X(t), Y(t), t \geq 0$ be standard Brownian motions starting at $x,y$ respectively. Find the distribution of the total time $T=Leb\{t \in [0,1]: X(t) \times Y(t) >0\}$, when $x=y=0$, i.e., the occupation time of the union of the first and third quadrants. If two adjacent quadrants are used, the problem becomes much easier and the distribution of $T$ follows the arcsine law.
Philip Ernst - One of the best experts on this subject based on the ideXlab platform.
-
on occupation times of the first and third quadrants for planar brownian motion
Journal of Applied Probability, 2017Co-Authors: Philip Ernst, Larry SheppAbstract:In Bingham and Doney (1988) the authors presented the Applied Probability community with a question which is very simply stated, yet is extremely difficult to solve: what is the distribution of the quadrant occupation time of planar Brownian motion? In this paper we study an alternate formulation of this long-standing open problem: let X ( t ), Y ( t ) t ≥0, be standard Brownian motions starting at x , y , respectively. Find the distribution of the total time T =Leb{ t ∈[0,1]: X ( t )× Y ( t )>0}, when x = y =0, i.e. the occupation time of the union of the first and third quadrants. If two adjacent quadrants are used, the problem becomes much easier and the distribution of T follows the arcsine law.
-
on occupation times of the first and third quadrants for planar brownian motion
arXiv: Probability, 2016Co-Authors: Philip Ernst, Larry SheppAbstract:An open problem of interest, first infused into the Applied Probability community in the work of Bingham and Doney in 1988, (see \cite{Bingham}) is stated as follows: find the distribution of the quadrant occupation time of planar Brownian motion. In this short communication, we study an alternate formulation of this longstanding open problem: let $X(t), Y(t), t \geq 0$ be standard Brownian motions starting at $x,y$ respectively. Find the distribution of the total time $T=Leb\{t \in [0,1]: X(t) \times Y(t) >0\}$, when $x=y=0$, i.e., the occupation time of the union of the first and third quadrants. If two adjacent quadrants are used, the problem becomes much easier and the distribution of $T$ follows the arcsine law.
Jose Garrido - One of the best experts on this subject based on the ideXlab platform.
-
on a general class of renewal risk process analysis of the gerber shiu function
Advances in Applied Probability, 2005Co-Authors: Jose GarridoAbstract:We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a Kn distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n ∈ ∌). The Laplace transform of the expected discounted penalty function at ruin is derived. This leads to a generalization of the defective renewal equations given by Willmot (1999) and Gerber and Shiu (2005). Finally, explicit results are given for rationally distributed claim severities. © Applied Probability Trust 2005.
Chuancun Yin - One of the best experts on this subject based on the ideXlab platform.
-
on optimality of the barrier strategy for a general levy risk process
Mathematical and Computer Modelling, 2011Co-Authors: Kam Chuen Yuen, Chuancun YinAbstract:We consider the optimal dividend problem for the insurance risk process in a general Levy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Levy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. [F. Avram, Z. Palmowski, M.R. Pistorius, On the optimal dividend problem for a spectrally negative Levy process, The Annals of Applied Probability 17 (2007) 156-180], Loeffen [R. Loeffen, On optimality of the barrier strategy in De Finetti's dividend problem for spectrally negative Levy processes, The Annals of Applied Probability 18 (2008) 1669-1680] and Kyprianou et al. [A.E. Kyprianou, V. Rivero, R. Song, Convexity and smoothness of scale functions with applications to De Finetti's control problem, Journal of Theoretical Probability 23 (2010) 547-564] in which the same problem was considered under the spectrally negative Levy processes setting.
-
on optimality of the barrier strategy for a general levy risk process
arXiv: Probability, 2011Co-Authors: Kam Chuen Yuen, Chuancun YinAbstract:We consider the optimal dividend problem for the insurance risk process in a general Levy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Levy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. (2007) [Annals of Applied Probability 17, 156-180], Loeffen (2008) [Annals of Applied Probability 18, 1669-1680] and Kyprianou et al. (2010) [Journal of Theoretical Probability 23, 547-564] in which the same problem was considered under the spectrally negative Levy processes setting.