5,062 research outputs found
Minimal Supersolutions of BSDEs with Lower Semicontinuous Generators
We study the existence and uniqueness of minimal supersolutions of backward
stochastic differential equations with generators that are jointly lower
semicontinuous, bounded below by an affine function of the control variable and
satisfy a specific normalization property
Minimal supersolutions of convex BSDEs
We study the nonlinear operator of mapping the terminal value to the
corresponding minimal supersolution of a backward stochastic differential
equation with the generator being monotone in , convex in , jointly lower
semicontinuous and bounded below by an affine function of the control variable
. We show existence, uniqueness, monotone convergence, Fatou's lemma and
lower semicontinuity of this operator. We provide a comparison principle for
minimal supersolutions of BSDEs.Comment: Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
We consider the Galerkin boundary element method (BEM) for weakly-singular
integral equations of the first-kind in 2D. We analyze some residual-type a
posteriori error estimator which provides a lower as well as an upper bound for
the unknown Galerkin BEM error. The required assumptions are weak and allow for
piecewise smooth parametrizations of the boundary, local mesh-refinement, and
related standard piecewise polynomials as well as NURBS. In particular, our
analysis gives a first contribution to adaptive BEM in the frame of
isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm
which steers the local mesh-refinement and the multiplicity of the knots.
Numerical experiments underline the theoretical findings and show that the
proposed adaptive strategy leads to optimal convergence
Introducing shrinkage in heavy-tailed state space models to predict equity excess returns
We forecast S&P 500 excess returns using a flexible Bayesian econometric
state space model with non-Gaussian features at several levels. More precisely,
we control for overparameterization via novel global-local shrinkage priors on
the state innovation variances as well as the time-invariant part of the state
space model. The shrinkage priors are complemented by heavy tailed state
innovations that cater for potential large breaks in the latent states.
Moreover, we allow for leptokurtic stochastic volatility in the observation
equation. The empirical findings indicate that several variants of the proposed
approach outperform typical competitors frequently used in the literature, both
in terms of point and density forecasts
Transfer Problem Dynamics: Macroeconomics of the Franco-Prussian War Indemnity
We study the classic transfer problem of predicting the effects of an international transfer on the terms of trade and the current account. A two-country model with debt and capital allows for realistic features of historical transfers: they follow wartime increases in government spending and are financed partly by borrowing. The model is applied to the largest historical transfer, the Franco-Prussian War indemnity of 1871-1873. In these three years, France transferred to Germany an amount equal to 22 percent of a year's GDP. When the transfer is combined with measured shocks to fiscal policy and a proxy for productivity shocks over the period, the model provides a very close fit to the historical sample paths of French GDP, terms of trade, net exports, and aggregate consumption. This makes a strong case for the dynamic general equilibrium approach to studying the transfer problem.transfer problem, current account, terms of trade
Minimal Supersolutions of Convex BSDEs under Constraints
We study supersolutions of a backward stochastic differential equation, the
control processes of which are constrained to be continuous semimartingales of
the form . The generator may depend on the
decomposition and is assumed to be positive, jointly
convex and lower semicontinuous, and to satisfy a superquadratic growth
condition in and . We prove the existence of a
supersolution that is minimal at time zero and derive stability properties of
the non-linear operator that maps terminal conditions to the time zero value of
this minimal supersolution such as monotone convergence, Fatou's lemma and
-lower semicontinuity. Furthermore, we provide duality results within the
present framework and thereby give conditions for the existence of solutions
under constraints.Comment: 23 page
- …