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  1. Research

    Measure distorted arrival rate risks and their rewards

    Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps. A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level. Es...

    Dilip B. Madan

    Probability, Uncertainty and Quantitative Risk 2017 2:8

    Published on: 26 June 2017

  2. Commentary

    A brief history of quantitative finance

    In this introductory paper to the issue, I will travel through the history of how quantitative finance has developed and reached its current status, what problems it is called to address, and how they differ f...

    Mauro Cesa

    Probability, Uncertainty and Quantitative Risk 2017 2:6

    Published on: 5 June 2017

  3. Research

    Backward stochastic differential equations with Young drift

    We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q∈[1,2). In contrast to previous work, we apply a direct fixpoin...

    Joscha Diehl and Jianfeng Zhang

    Probability, Uncertainty and Quantitative Risk 2017 2:5

    Published on: 5 June 2017

  4. Research

    Implied fractional hazard rates and default risk distributions

    Default probability distributions are often defined in terms of their conditional default probability distribution, or their hazard rate. By their definition, they imply a unique probability density function. ...

    Charles S. Tapiero and Pierre Vallois

    Probability, Uncertainty and Quantitative Risk 2017 2:2

    Published on: 1 March 2017

  5. Research

    Convergence to a self-normalized G-Brownian motion

    G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion. Its quadratic variation process is also a continuous process with independent and st...

    Zhengyan Lin and Li-Xin Zhang

    Probability, Uncertainty and Quantitative Risk 2017 2:4

    Published on: 1 March 2017

  6. Research

    A branching particle system approximation for a class of FBSDEs

    In this paper, a new numerical scheme for a class of coupled forward-backward stochastic differential equations (FBSDEs) is proposed by using branching particle systems in a random environment. First, by the f...

    Dejian Chang, Huili Liu and Jie Xiong

    Probability, Uncertainty and Quantitative Risk 2016 1:9

    Published on: 1 December 2016

  7. Research

    Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs

    In this paper, we propose a new type of viscosity solutions for fully nonlinear path-dependent PDEs. By restricting the solution to a pseudo-Markovian structure defined below, we remove the uniform non-degener...

    Ibrahim Ekren and Jianfeng Zhang

    Probability, Uncertainty and Quantitative Risk 2016 1:6

    Published on: 1 December 2016

  8. Editorial

    Editorial

    Shige Peng, Rainer Buckdahn and Juan Li

    Probability, Uncertainty and Quantitative Risk 2016 1:5

    Published on: 16 August 2016

  9. Research

    On approximation of BSDE and multi-step MLE-processes

    We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case. We suppose that the forward equation depends on some unknown finite-dimensional par...

    Yu A. Kutoyants

    Probability, Uncertainty and Quantitative Risk 2016 1:4

    Published on: 16 August 2016

  10. Research

    Pathwise no-arbitrage in a class of Delta hedging strategies

    We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer’s pathwise Itô calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations an...

    Alexander Schied and Iryna Voloshchenko

    Probability, Uncertainty and Quantitative Risk 2016 1:3

    Published on: 16 August 2016

  11. Research

    Portfolio theory for squared returns correlated across time

    Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two-period conic...

    Ernst Eberlein and Dilip B. Madan

    Probability, Uncertainty and Quantitative Risk 2016 1:1

    Published on: 16 August 2016

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