On optimal investiment strategies

Suppose an investor has a fixed decision horizon and an appropriate utility function for measuring his or her utility of wealth. If there are only two investment vehicles, a risky and a risk-free asset, then the optimal investment strategy is such that, at any time, the amount invested in the risky asset must be the product of his or her “current risk tolerance” and the risk premium on the risky asset, divided by the square of the diffusion coefficient of the risky asset. In the case of more than one risky asset, the optimal investment strategy is similar, with the ratios of the amounts invested in the different risky assets being constant over time.     

Tofacitinib in the treatment of moderate-to-severe rheumatoid arthritis: a cost-effectiveness analysis compared with adalimumab in Taiwan

Aims: Tofacitinib is an oral Janus kinase inhibitor for the treatment of rheumatoid arthritis (RA). This analysis investigated the cost-effectiveness of the second-line treatment with tofacitinib, compared with adalimumab, both plus methotrexate (MTX), in patients with moderate-to-severe RA and an inadequate response to the first-line MTX, from a Taiwan National Health Insurance Administration perspective.

Materials and methods: A patient-level simulation model was used to project lifetime costs and quality-adjusted life-years (QALYs). Base-case analysis compared second-line treatment with tofacitinib 5?mg twice daily plus MTX vs adalimumab 40?mg every 2?weeks plus MTX. Patients switched or discontinued treatment due to a lack or loss of effectiveness or a serious adverse event. Efficacy was measured by change in Health Assessment Questionnaire-Disability Index (HAQ-DI) score. HAQ-DI scores were used to predict mortality and resource utilization, and were mapped onto utility values to estimate QALYs. Efficacy and safety data were derived from clinical trials and other secondary sources. Uncertainty in model parameters was explored using one-way deterministic and probabilistic sensitivity analyses.

Results: Patients gained 0.09 more QALYs with second-line tofacitinib plus MTX compared with adalimumab plus MTX (5.13 vs 5.04, respectively) at an additional cost of New Taiwan Dollars (NT$) 12,881. The incremental cost-effectiveness ratio was NT$143,122/QALY. One-way sensitivity analysis confirmed the base-case result was robust.

Limitations: The lack of available clinical data, particularly for HAQ-DI scores, may introduce some bias in the analysis. No patients were in an early stage of RA, which may limit the generalizability of these results. Base-case results from our study are not necessarily generalizable to countries with healthcare systems that differ considerably from Taiwan.

Conclusions: From a payer perspective, second-line treatment with tofacitinib plus MTX is a cost-effective treatment strategy, compared with adalimumab plus MTX, in patients with moderate-to-severe RA in Taiwan.

Trial registration: ClinicalTrials.gov identifier: NCT00853385.     

Extending the enterprise evolution contextualisation model

Enterprise engineering (EE) emerged as a new discipline to encourage comprehensive and consistent enterprise design. Since EE is multidisciplinary, various researchers study enterprises from different perspectives, which resulted in a plethora of applicable literature and terminology, but without shared meaning. Previous research specifically focused on the fragmentation of knowledge for designing and aligning the information and communication technology (ICT) subsystem of the enterprise in order to support the business organisation subsystem of the enterprise. As a solution for this fragmented landscape, a business-IT alignment model (BIAM) was developed inductively from existing business-IT alignment approaches. Since most of the existing alignment frameworks addressed the alignment between the ICT subsystem and the business organisation subsystem, BIAM also focused on the alignment between these two subsystems. Yet, the emerging EE discipline intends to address a broader scope of design, evident in the existing approaches that incorporate a broader scope of design/alignment/governance. A need was identified to address the knowledge fragmentation of the EE knowledge base by adapting BIAM to an enterprise evolution contextualisation model (EECM), to contextualise a broader set of approaches, as identified by Lapalme. The main contribution of this article is the incremental development and evaluation of EECM. We also present guiding indicators/prerequisites for applying EECM as a contextualisation tool.     

Utility Functions

Abstract

This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility function). The postulate of equivalent expected utility can be used to replace a random gain by a fixed amount and to determine a fair premium for claims to be insured, even if the insurer’s wealth without the new contract is a random variable itself. Then n companies (or economic agents) with random wealth are considered. They are interested in exchanging wealth to improve their expected utility. The family of Pareto optimal risk exchanges is characterized by the theorem of Borch. Two specific solutions are proposed. The first, believed to be new, is based on the synergy potential; this is the largest amount that can be withdrawn from the system without hurting any company in terms of expected utility. The second is the economic equilibrium originally proposed by Borch. As by-products, the option-pricing formula of Black-Scholes can be derived and the Esscher method of option pricing can be explained.     

Pricing Perpetual Options for Jump Processes

Abstract

We consider two models in which the logarithm of the price of an asset is a shifted compound Poisson process. Explicit results are obtained for prices and optimal exercise strategies of certain perpetual American options on the asset, in particular for the perpetual put option. In the first model in which the jumps of the asset price are upwards, the results are obtained by the martingale approach and the smooth junction condition. In the second model in which the jumps are downwards, we show that the value of the strategy corresponding to a constant option-exercise boundary satisfies a certain renewal equation. Then the optimal exercise strategy is obtained from the continuous junction condition. Furthermore, the same model can be used to price certain reset options. Finally, we show how the classical model of geometric Brownian motion can be obtained as a limit and also how it can be integrated in the two models.