Simulation based policy iteration for American style derivatives --- A multilevel approach

This paper presents a novel approach to reduce the complexity of simulation based policy iteration methods for pricing American options. Typically, Monte Carlo construction of an improved policy gives rise to a nested simulation algorithm for the price of the American product. In this respect our new approach uses the multilevel idea in the context of the inner simulations required, where each level corresponds to a specific number of inner simulations. A thorough analysis of the crucial convergence rates in the respective multilevel policy improvement algorithm is presented. A detailed complexity analysis shows that a significant reduction in computational effort can be achieved in comparison to standard Monte Carlo based policy iteration

Libor model with expiry-wise stochastic volatility and displacement

We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-strike panel at the market. However, since even after freezing the Libors in the drift of this model, the Libor dynamics are not affine, new affine approximations have to be developed in order to obtain Fourier based (approximate) pricing procedures for caps and swaptions. As a result, we end up with a Libor modeling package that allows for efficient calibration to a complete system of cap/swaption market quotes that performs well even in crises times, where structural breaks in vola-strike-maturity panels are typically observed.Comment: 3 tables, 10 figure

Efficient production of the Nylon 12 monomer ω-aminododecanoic acid methyl ester from renewable dodecanoic acid methyl ester with engineered Escherichia coli

The expansion of microbial substrate and product scopes will be an important brick promoting future bioeconomy. In this study, an orthogonal pathway running in parallel to native metabolism and converting renewable dodecanoic acid methyl ester (DAME) via terminal alcohol and aldehyde to 12-aminododecanoic acid methyl ester (ADAME), a building block for the high-performance polymer Nylon 12, was engineered in Escherichia coli and optimized regarding substrate uptake, substrate requirements, host strain choice, flux, and product yield. Efficient DAME uptake was achieved by means of the hydrophobic outer membrane porin AlkL increasing maximum oxygenation and transamination activities 8.3 and 7.6-fold, respectively. An optimized coupling to the pyruvate node via a heterologous alanine dehydrogenase enabled efficient intracellular L-alanine supply, a prerequisite for self-sufficient whole-cell transaminase catalysis. Finally, the introduction of a respiratory chain-linked alcohol dehydrogenase enabled an increase in pathway flux, the minimization of undesired overoxidation to the respective carboxylic acid, and thus the efficient formation of ADAME as main product. The completely synthetic orthogonal pathway presented in this study sets the stage for Nylon 12 production from renewables. Its effective operation achieved via fine tuning the connectivity to native cell functionalities emphasizes the potential of this concept to expand microbial substrate and product scopes

SDE based regression for random PDEs

A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour

Robust optimal stopping

This paper studies the optimal stopping problem in the presence of model uncertainty (ambiguity). We develop a method to practically solve this problem in a general setting, allowing for general time-consistent ambiguity averse preferences and general payoff processes driven by jump-diffusions. Our method consists of three steps. First, we construct a suitable Doob martingale associated with the solution to the optimal stopping problem represented by the Snell envelope using backward stochastic calculus. Second, we employ this martingale to construct an approximated upper bound to the solution using duality. Third, we introduce backward-forward simulation to obtain a genuine upper bound to the solution, which converges to the true solution asymptotically. We analyze the asymptotic behavior and convergence properties of our method. We illustrate the generality and applicability of our method and the potentially significant impact of ambiguity to optimal stopping in a few examples

Optimal stopping under uncertainty in drift and jump intensity

This paper studies the optimal stopping problem in the presence of model uncertainty (ambiguity). We develop a numerically implementable method to solve this problem in a general setting, allowing for general time-consistent ambiguity-averse preferences and general payoff processes driven by jump diffusions. Our method consists of three steps. First, we construct a suitable Doob martingale associated with the solution to the optimal stopping problem using backward stochastic calculus. Second, we employ this martingale to construct an approximated upper bound to the solution using duality. Third, we introduce backward-forward simulation to obtain a genuine upper bound to the solution, which converges to the true solution asymptotically. We also provide asymptotically optimal exercise rules. We analyze the limiting behavior and convergence properties of our method. We illustrate the generality and applicability of our method and the potentially significant impact of ambiguity to optimal stopping in a few examples