This review gives a survey on the latest most representative developments and progress concerning ionic liquids, from their fundamental properties to their applications in catalytic processes. It also highlights their emerging use for biomass treatment and transformation.

Ionic liquids and catalysis: Recent progress from knowledge to applications

Recent advances in ionic liquid catalysis

Preliminaries from Probability Theory.- Statistical Methods.- Modeling via Stochastic Processes.- Diffusion Processes.- Martingales and Stochastic Integrals.- The Ito Formula.- Stochastic Differential Equations.- to Option Pricing.- Various Approaches to Asset Pricing.- Continuous Financial Markets.- Portfolio Optimization.- Modeling Stochastic Volatility.- Minimal Market Model.- Markets with Event Risk.- Numerical Methods.- Solutions for Exercises.

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A Benchmark Approach to Quantitative Finance

Publisher Summary This chapter dealt mainly with the application of financial pricing techniques to insurance problems. However, actuarial concepts are also of increasing relevance for finance problems. This chapter presents that realistic models for asset price processes are typically incomplete. Actuarial concepts for risk-management might prove helpful in dealing with these “unhedgeable” risks. An example where such concepts are already applied, is the RAC-(risk adjusted capital) approach in insurance that has become popular among investment banks as a tool for the determination of risk capital and capital allocations. It is no coincidence that Swiss Bank Cooperation (now UBS) called one of its credit risk management systems ACRA, which stands for Actuarial Credit Risk Accounting.

Stochastic processes in insurance and finance

Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of single-period variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.

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Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis

We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process. Then we present stochastic numerical methods permitting the explicit computation of option prices and hedging strategies, and we illustrate our approach by specific examples.

Option Pricing Under Incompleteness and Stochastic Volatility

Option pricing under incompleteness and stochastic volatility.

The Optimal Discretization of Stochastic Differential Equations

We study the pathwise (strong) approximation of scalar stochastic differential equations with respect to the global error in the L2-norm. For equations with additive noise we establish a sharp lower error bound in the class of arbitrary methods that use a fixed number of observations of the driving Brownian motion. As a consequence, higher order methods do not exist if the global error is analyzed. We introduce an adaptive step-size control for the Euler scheme which performs asymptotically optimally. In particular, the new method is more efficient than an equidistant discretization. This superiority is confirmed in simulation experiments for equations with additive noise, as well as for general scalar equations.

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Optimal approximation of stochastic differential equations by adaptive step-size control

The platinum-catalyzed hydrosilylation of allyl chloride with trichlorosilane was investigated in an ionic liquid-organic biphasic reaction mode. After an ionic liquid screening and repetitive batch mode experiments, the process was realized in a continuous mode using a loop reactor concept with integrated continuous separation and recycling of the ionic liquid catalyst phase. The continuous reactor could be operated for 48 h at constant activity and selectivity without addition of platinum indicating that platinum leaching into the product phase was far below 1 ppm. Enhanced selectivity for the product trichloro(3-chloropropyl)silane (compared to the state-of-the art) and the possibility to use simple platinum tetrachloride (PtCl 4 ) as platinum source are further attractive features of this new ionic liquid-based process concept.

Liquid‐Liquid Biphasic, Platinum‐Catalyzed Hydrosilylation of Allyl Chloride with Trichlorosilane using an Ionic Liquid Catalyst Phase in a Continuous Loop Reactor

Norbert Hofmann

Papers

Option Pricing Under Incompleteness and Stochastic Volatility

Option pricing under incompleteness and stochastic volatility.

The Optimal Discretization of Stochastic Differential Equations

Optimal approximation of stochastic differential equations by adaptive step-size control

Liquid‐Liquid Biphasic, Platinum‐Catalyzed Hydrosilylation of Allyl Chloride with Trichlorosilane using an Ionic Liquid Catalyst Phase in a Continuous Loop Reactor