2,376 research outputs found
The stochastic goodwill problem
Stochastic control problems related to optimal advertising under uncertainty
are considered. In particular, we determine the optimal strategies for the
problem of maximizing the utility of goodwill at launch time and minimizing the
disutility of a stream of advertising costs that extends until the launch time
for some classes of stochastic perturbations of the classical Nerlove-Arrow
dynamics. We also consider some generalizations such as problems with
constrained budget and with discretionary launching
Nonparametric estimates of pricing functionals
We analyze the empirical performance of several non-parametric estimators of
the pricing functional for European options, using historical put and call
prices on the S&P500 during the year 2012. Two main families of estimators are
considered, obtained by estimating the pricing functional directly, and by
estimating the (Black-Scholes) implied volatility surface, respectively. In
each case simple estimators based on linear interpolation are constructed, as
well as more sophisticated ones based on smoothing kernels, \`a la
Nadaraya-Watson. The results based on the analysis of the empirical pricing
errors in an extensive out-of-sample study indicate that a simple approach
based on the Black-Scholes formula coupled with linear interpolation of the
volatility surface outperforms, both in accuracy and computational speed, all
other methods
Well-posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise
We establish well-posedness in the mild sense for a class of stochastic
semilinear evolution equations with a polynomially growing quasi-monotone
nonlinearity and multiplicative Poisson noise. We also study existence and
uniqueness of invariant measures for the associated semigroup in the Markovian
case. A key role is played by a new maximal inequality for stochastic
convolutions in spaces.Comment: Final versio
On uniqueness of mild solutions for dissipative stochastic evolution equations
In the semigroup approach to stochastic evolution equations, the fundamental
issue of uniqueness of mild solutions is often "reduced" to the much easier
problem of proving uniqueness for strong solutions. This reduction is usually
carried out in a formal way, without really justifying why and how one can do
that. We provide sufficient conditions for uniqueness of mild solutions to a
broad class of semilinear stochastic evolution equations with coefficients
satisfying a monotonicity assumption.Comment: 10 page
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