11,183 research outputs found
Application of Operator Splitting Methods in Finance
Financial derivatives pricing aims to find the fair value of a financial
contract on an underlying asset. Here we consider option pricing in the partial
differential equations framework. The contemporary models lead to
one-dimensional or multidimensional parabolic problems of the
convection-diffusion type and generalizations thereof. An overview of various
operator splitting methods is presented for the efficient numerical solution of
these problems.
Splitting schemes of the Alternating Direction Implicit (ADI) type are
discussed for multidimensional problems, e.g. given by stochastic volatility
(SV) models. For jump models Implicit-Explicit (IMEX) methods are considered
which efficiently treat the nonlocal jump operator. For American options an
easy-to-implement operator splitting method is described for the resulting
linear complementarity problems.
Numerical experiments are presented to illustrate the actual stability and
convergence of the splitting schemes. Here European and American put options
are considered under four asset price models: the classical Black-Scholes
model, the Merton jump-diffusion model, the Heston SV model, and the Bates SV
model with jumps
Self-Employment, Family Background, and Race
We focus on the intergenerational transmission of the propensity to be self-employed. Our emphasis is on the role of family background, and in particular, on what we call the intergenerational pick-up rate with respect to self-employment, the probability that a person with a self-employed parent will become self-employed him or herself. We use the General Social Survey, a data source with rich information on individuals' family histories, to investigate how family background affects self-employment probabilities and to document how racial and ethnic groups differ with respect to the intergenerational pick-up rate. We confirm earlier findings that father's self-employment status is an important determinant of offspring's self-employment outcomes. New results include: 1) The impact of paternal self-employment differs by race. 2) Even independent of father's occupation, family structure plays a role. 3) Blacks have lower self-employment rates than whites in part because they have different family structures; still, within each family type, blacks have lower self-employment rates. 4) Extrapolating current patterns into the future, there is no indication that black and white self-employment rates will converge any time soon. 5) The relatively high self-employment rates of immigrants carry into the next generation, but not beyond that. 6) Male immigrants who have self-employed fathers re no more likely to be self-employed than other immigrants.
The power-series algorithm for Markovian queueing networks
A newversion of the Power-Series Algorithm is developed to compute the steady-state distribution of a rich class of Markovian queueing networks. The arrival process is a Multi-queue Markovian Arrival Process, which is a multi-queue generalization of the BMAP. It includes Poisson, fork and round-robin arrivals. At each queue the service process is a Markovian Service Process, which includes sequences of phase-type distributions, setup times and multi-server queues. The routing is Markovian. The resulting queueing network model is extremely general, which makes the Power-Series Algorithm a useful tool to study load-balancing, capacity-assignment and sequencing problems.Queueing Network;operations research
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