Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic programming lifted these ideas to first order logic using several representation schemes. Recent work introduced a first order variant of d...

Let H̄ , Ḡ, and H̄ be survival functions satisfying the constraint F̄ ≤ H̄≤Ḡ. Lee, Yan, and Shi (1999) had developed an algorithm to estimate the survival function H̄ when F̄ and Ḡ are known. However, lacking a closed form of the estimator makes the investigations of the properties of the estimators difficult. In this paper, we propose alternative estimators for H̄ in the case where F̄ and Ḡ are known....

[Abstract] In this project the order book model proposed by Cont et al. [10] is used as a starting point to model order book dynamics. This model nicely combines three desirable properties from earlier studies: it is easy to calibrate, it reproduces statistical properties of the order book and it allows to make analytical computations in the order book. The model is studied, calibrated and test...

A traditional random variable X is a function that maps from a stochastic process to the real line. Here, “real line” refers to the structure (R, |⋅|, ≤) , where R is the set of real numbers, ≤ is the standard linear order relation on R , and d (x, y) ≜ |x − y| is the usual metric on R . The traditional expectation value E(X) of X is thenoften apoor choice of a statisticwhen the stochastic proc...

We seek numerical methods for second-order stochastic differential equations that accurately reproduce the stationary distribution for all values of damping. A complete analysis is possible for linear second-order equations (damped harmonic oscillators with noise), where the statistics are Gaussian and can be calculated exactly in the continuous-time and discrete-time cases. A matrix equation i...

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that depend only loga...

Limit distribution results on quadratic and higher order variation quantities are derived for certain types of continuous local martingales, in particular for a class of OU-based stochastic volatility models. Some key words: Mixed asymptotic normality; Realised volatility; Quadratic variation.

We present a Petri net formalism that allows for mixed discrete and continuous stochastic models. The continuous part of the models consists of uid places that are lled and emptied at random (normally distributed) rate. Fluid places can be used for the modelling of continuous system components as well as for continuous approximation of heavily loaded discrete places in order to avoid state spac...

We propose a stochastic model for the continuous-time dynamics of a limit order book. The model strikes a balance between two desirable features: it captures key empirical properties of order book dynamics and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on hig...