Probability, Uncertainty and Quantitative Risk
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A branching particle system approximation for a class of FBSDEs
Probability, Uncertainty and Quantitative Risk - Tập 1 - Trang 1-34 - 2016
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 four step scheme, we
introduce a partial differential Eq. (PDE) used to represent the solution of the
FBSDE system. Then, infinite and finite particle systems are constructed to
obtain the app...
Mixed deterministic and random optimal control of linear stochastic systems with quadratic costs
Probability, Uncertainty and Quantitative Risk - Tập 4 Số 1 - 2019
Measure distorted arrival rate risks and their rewards
Probability, Uncertainty and Quantitative Risk - Tập 2 - Trang 1-21 - 2017
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. Estimation is done by
matrix exponentiation of the transition rate matrix for a continuous time finite
state Markov chain approximation. The motion is decomposed into a space
dependent drift an...
Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle
Probability, Uncertainty and Quantitative Risk - Tập 3 - Trang 1-37 - 2018
We study the existence and uniqueness of a solution to path-dependent backward
stochastic Volterra integral equations (BSVIEs) with jumps, where
path-dependence means the dependence of the free term and generator of a path of
a càdlàg process. Furthermore, we prove path-differentiability of such a
solution and establish the duality principle between a linear path-dependent
forward stochastic Volte...
Backward-forward linear-quadratic mean-field games with major and minor agents
Probability, Uncertainty and Quantitative Risk - Tập 1 Số 1 - 2016
Law of large numbers and central limit theorem under nonlinear expectations
Probability, Uncertainty and Quantitative Risk - Tập 4 - Trang 1-8 - 2019
The main achievement of this paper is the finding and proof of Central Limit
Theorem (CLT, see Theorem 12) under the framework of sublinear expectation.
Roughly speaking under some reasonable assumption, the random sequence
$\{1/\sqrt {n}(X_{1}+\cdots +X_{n})\}_{i=1}^{\infty }$ converges in law to a
nonlinear normal distribution, called G-normal distribution, where
$\{X_{i}\}_{i=1}^{\infty }$ is a...
Moderate deviation for maximum likelihood estimators from single server queues
Probability, Uncertainty and Quantitative Risk - Tập 5 - Trang 1-13 - 2020
Consider a single server queueing model which is observed over a continuous time
interval (0,T], where T is determined by a suitable stopping rule. Let θ be the
unknown parameter for the arrival process and $\hat {\theta }_{T}$ be the
maximum likelihood estimator of θ. The main goal of this paper is to obtain a
moderate deviation result of the maximum likelihood estimator for the single
server que...
Financial asset price bubbles under model uncertainty
Probability, Uncertainty and Quantitative Risk - Tập 2 - Trang 1-29 - 2017
We study the concept of financial bubbles in a market model endowed with a set
${\mathcal {P}}$ of probability measures, typically mutually singular to each
other. In this setting, we investigate a dynamic version of robust
superreplication, which we use to introduce the notions of bubble and robust
fundamental value in a way consistent with the existing literature in the
classical case ${\mathcal...
The Cauchy problem of Backward Stochastic Super-Parabolic Equations with Quadratic Growth
Probability, Uncertainty and Quantitative Risk - Tập 4 Số 1 - 2019
Portfolio theory for squared returns correlated across time
Probability, Uncertainty and Quantitative Risk - Tập 1 - Trang 1-36 - 2016
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 portfolio
problem is formulated and implemented. This development leads to a mean ask
price frontier, where the latter employs concave distortions. The modeling
permits access to skewness vi...
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