Two-dimensional turbulent flow chromatography coupled on-line to liquid chromatography–mass spectrometry for solution-based ligand screening against multiple proteins

We present herein a novel bioseparation/chemical analysis strategy for protein–ligand screening and affinity ranking in compound mixtures, designed to increase screening rates and improve sensitivity and ruggedness in performance. The strategy is carried out by combining on-line two-dimensional turbulent flow chromatography (2D-TFC) with liquid chromatography–mass spectrometry (LC–MS), and accomplished through the following steps: (1) a reversed-phase TFC stage to separate the protein/ligand complex from the unbound free molecules, (2) an on-line dissociation process to release the bound ligands from the complexes, and (3) a second mixed-mode cation-exchange/reversed-phase TFC stage to trap the bound ligands and to remove the proteins and salts, followed by LC–MS analysis for identification and determination of the binding affinities. The technique can implement an ultra-fast isolation of protein/ligand complex with the retention time of a complex peak in about 5 s, and on-line prepare the “clean” sample to be directly compatible with the LC–MS analysis. The improvement in performance of this 2D-TFC/LC–MS approach over the conventional approach has been demonstrated by determining affinity-selected ligands of the target proteins acetylcholinesterase and butyrylcholinesterase from a small library with known binding affinities and a steroidal alkaloid library composed of structurally similar compounds. Our results show that 2D-TFC/LC–MS is a generic and efficient tool for high-throughput screening of ligands with low-to-high binding affinities, and structure-activity relationship evaluation.     

On a dual model with a dividend threshold

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integro-differential equations satisfied by the expected total discounted dividends until ruin and show how the equations can be solved by using only one of the two integro-differential equations. The cases where profits follow an exponential or a mixture of exponential distributions are then solved and the discussion for the case of a general profit distribution follows by the use of Laplace transforms. We illustrate how the optimal threshold level that maximizes the expected total discounted dividends until ruin can be obtained, and finally we generalize the results to the case where the surplus process is a more general skip-free downwards Lévy process.     

Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

Opportunistic timing and manipulation in Australian Federal Elections

In many parliamentary systems, election timing is an important decision made by governments in order to maximize their expected remaining life in power. Governments can also introduce policy or economic actions to enhance their popular standing and thus their chance of being re-elected. On the other hand, an oppositions’ natural objective is to gain power, and they will also apply controls through their own policies to reduce the governments’ chance of being re-elected. In this paper we employ a dynamic programming approach to determine the optimal timing for governments and oppositions to best utilize their limited resources. At each decision branch, the optimal control is interpreted as a Nash–Cournot equilibrium of a zero-sum political game which, in certain states, admits mixed strategy solutions. We perform a case study on the Australian Federal Election for House of Representatives.     

Explicit portfolio for unit-linked life insurance contracts with surrender option

Introducing a surrender option in unit-linked life insurance contracts leads to a dependence between the surrender time and the financial market. [J. Barbarin, Risk minimizing strategies for life insurance contracts with surrender option, Tech. rep., University of Louvain-La-Neuve, 2007] used a lot of concepts from credit risk to describe the surrender time in order to hedge such types of contracts. The basic assumption made by Barbarin is that the surrender time is not a stopping time with respect to the financial market.The goal of this article is to make the hedging strategies more explicit by introducing concrete processes for the risky asset and by restricting the hazard process to an absolutely continuous process.First, we assume that the risky asset follows a geometric Brownian motion. This extends the theory of [T. Møller, Risk-minimizing hedging strategies for insurance payment processes, Finance and Stochastics 5 (2001) 419–446], in that the random times of payment are not independent of the financial market. Second, the risky asset follows a Lévy process.For both cases, we assume the payment process contains a continuous payment stream until surrender or maturity and a payment at surrender or at maturity, whichever comes first.     

A fast Petrov–Galerkin method for solving the generalized airfoil equation

In this paper we develop a fast Petrov–Galerkin method for solving the generalized airfoil equation using the Chebyshev polynomials. The conventional method for solving this equation leads to a linear system with a dense coefficient matrix. When the order of the linear system is large, the computational complexity for solving the corresponding linear system is huge. For this we propose the matrix truncation strategy, which compresses the dense coefficient matrix into a sparse matrix. We prove that the truncated method preserves the optimal order of the approximate solution for the conventional method. Moreover, we solve the truncated equation using the multilevel augmentation method. The computational complexity for solving this truncated linear system is estimated to be linear up to a logarithmic factor.     

Optimal consumption and investment with insurer default risk

We solve the optimal consumption and investment problem in an incomplete market, where borrowing constraints and insurer default risk are considered jointly. We derive in closed-form the optimal consumption and investment strategies. We find two main results by quantitative analysis. As insurer default risk increases, the proportion of wealth invested in stocks could increase when wealth is small, and decrease when wealth is large. As risk aversion increases, the voluntary annuity demand could increase when insurer default risk is low, and decrease when this risk is high.     

Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion

This paper considers the robust equilibrium reinsurance and investment strategies for an ambiguity-averse insurer under a dynamic mean–variance criterion. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of a risk-free asset and a credit default swap (CDS). Following a game theoretic approach, robust equilibrium strategies and equilibrium value functions for the pre-default case and the post-default case are derived, respectively. For the ambiguity-averse insurer, in general the equilibrium strategies can be characterized by unique solutions to some algebraic equations. For the degenerate case with an ambiguity-neutral insurer, closed-form expressions of equilibrium strategies and equilibrium value functions are obtained. Numerical examples demonstrate that the consideration of model uncertainty and CDS investment improves the insurer’s utility. In this regard, our paper establishes theoretical and numerical support for the importance of ambiguity aversion, credit risk and their interplay in insurance business.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

Procurement strategies for lost-sales inventory systems with all-units discounts

Despite the prevalence of all-units discounts in procurement contracts, these discounts pose a technical challenge to analyze procurement strategies due to neither concave nor convex ordering costs. In this paper, we consider the optimal procurement strategies with all-units discounts under the lost-sales setting. By assuming log-concave demands, we find that the optimal procurement strategies have a generalized Q-jump (s, S) structure by introducing a new notion of Q-jump single-crossing. In particular, a sufficient condition is provided for degenerating the optimal procurement strategies from a generalized Q-jump (s, S) structure into a Q-jump (s, S) structure, which is definitely optimal for the single-period problem. Extensive numerical results suggest that the Q-jump (s, S) policy as a heuristic performs considerably well when its optimality sufficient condition is violated. Our results can be extended to systems with multi-break all-units discounts, and systems with all-units discounts on batch ordering.