A note on Wick products and the fractional Black-Scholes model

In some recent papers (Elliott and van der Hoek 2003; Hu and Øksendal 2003) a fractional Black-Scholes model has been proposed as an improvement of the classical Black-Scholes model (see also Benth 2003; Biagini et al. 2002; Biagini and Øksendal 2004). Common to these fractional Black-Scholes models is that the driving Brownian motion is replaced by a fractional Brownian motion and that the Itô integral is replaced by the Wick integral, and proofs have been presented that these fractional Black-Scholes models are free of arbitrage. These results on absence of arbitrage complelety contradict a number of earlier results in the literature which prove that the fractional Black-Scholes model (and related models) will in fact admit arbitrage. The objective of the present paper is to resolve this contradiction by pointing out that the definition of the self-financing trading strategies and/or the definition of the value of a portfolio used in the above papers does not have a reasonable economic interpretation, and thus that the results in these papers are not economically meaningful. In particular we show that in the framework of Elliott and van der Hoek 2003, a naive buy-and-hold strategy does not in general qualify as self-financing. We also show that in Hu and Øksendal 2003, a portfolio consisting of a positive number of shares of a stock with a positive price may, with positive probability, have a negative value.Received: August 2004, Mathematics Subject Classification (2000): 91B28, 60H05JEL Classification: G10Support of the first author from the Jan Wallander and Tom Hedelius foundation is gratefully acknowledged. The research of the second author is supported by the Swedish Research Council.     

Exploring the potential value of improved care for secondary hyperparathyroidism with a novel calcimimetic therapy

Aims: This study explored the use of a value-based pricing approach for the new calcimimetic etelcalcetide indicated for the treatment of secondary hyperparathyroidism (SHPT) in patients receiving hemodialysis. It used the US payer perspective and applied the cost-effectiveness framework. Because etelcalcetide is an intravenous therapy that can be titrated for individual patients, and because its utilization is yet to be assessed in real world settings, a range of plausible doses were estimated for etelcalcetide to define a range of prices. These were either in relation to the existing oral calcimimetic cinacalcet or compared to no calcimimetic treatment.

Materials and methods: The value-based price of etelcalcetide was determined via a Markov model. This model combined data from the etelcalcetide trials and previously published cost-effectiveness models in SHPT, and allowed extrapolation of treatment effects on mortality, cardiovascular events, fracture, and parathyroidectomy. Several dosing scenarios were explored covering the dose ranges of 30.0–64.18?mg per day for cinacalcet and 1.07–3.11?mg per day for etelcalcetide. These included the mean dose from the etelcalcetide trials, the preliminary defined daily dose, and the expected most common dose in real world. An acceptable price range for etelcalcetide was assessed by comparing the incremental cost-effectiveness ratios obtained with the willingness-to-pay threshold range of $100,000–$300,000/quality-adjusted life-years.

Results: Cost-effectiveness analysis supported value-based prices for etelcalcetide ranging from $21.15–$49.97/mg vs cinacalcet, and $13.79–$119.45/mg vs no calcimimetics.

Limitations: There is uncertainty around what the real-world dosing will be for etelcalcetide. Another important nuance is that no studies have examined etelcalcetide effects on hard outcomes and, therefore, this modeling exercise relied on an extrapolation approach.

Conclusions: This cost-effectiveness analysis, including scenarios to address uncertainties, allowed estimation of a value-based price range to aid reimbursement decisions in the US.     

A Cost-effective Approach to Attracting Low-income Countries to International Emissions Trading: Theory and Experiments

The cost-effectiveness of the KyotoProtocol and any similar non-global treatywould be enhanced by attracting additionalcountries to international emissions tradingand achieving this as soon as possible. Incontrast to what is heard in most of thedebate, such an enlargement is here taken to beattained with the new participants, atleast to begin with, being fullycompensated. This paper focuses on twoforms of compensation that can be used toattract poor countries to participate inemissions trading. The theoretical aswell as experimental evidence suggests that, ifpoor countries are more risk averse than richcountries, partial compensation in terms offinancial transfers is more cost-effective thanrelying solely on compensation in kind –emission quotas – as has been the case so far.Using money for partial compensation would alsoreduce the risk for ``hot air' allocations andthe ensuing political obstacles tocost-effectiveness that such allocations tendto create.     

On time-inconsistent stochastic control in continuous time

In this paper, which is a continuation of the discrete-time paper (Björk and Murgoci in Finance Stoch. 18:545–592, 2004), we study a class of continuous-time stochastic control problems which, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We study these problems within a game-theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled continuous-time Markov process and a fairly general objective functional, we derive an extension of the standard Hamilton–Jacobi–Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy as well as the equilibrium value function. The main theoretical result is a verification theorem. As an application of the general theory, we study a time-inconsistent linear-quadratic regulator. We also present a study of time-inconsistency within the framework of a general equilibrium production economy of Cox–Ingersoll–Ross type (Cox et al. in Econometrica 53:363–384, 1985).     

Financial stress and economic activity in Germany

The financial crisis and the European sovereign debt crisis have shown that financial stress may be an important driver for economic activity. In this paper, I derive a financial stress index for Germany, using a dynamic approximate factor model that summarizes a stress component of various financial variables. Subsequently, I analyze the effects of financial stress on economic activity in a threshold vector autoregressive model. I find that if the index exceeds a certain threshold, an increase in financial stress causes economic activity to decelerate significantly, whereas if it is below this threshold, economic activity remains nearly unaffected.     

Analysis of the mechanism of injury in non-fatal vehicle-to-pedestrian and vehicle-to-bicyclist frontal crashes in Sweden

The aim of this paper is to analyse and compare injuries and injury sources in pedestrian and bicyclist non-fatal real-life frontal passengercar crashes, considering in what way pedestrian injury mitigation systems also might be adequate for bicyclists. Data from 203 non-fatal vehicle-to-pedestrian and vehicle-to-bicyclist crashes from 1997 through 2006 in a city in northern Sweden were analysed by use of the hospitals injury data base in addition to interviews with the injured. In vehicle-to-pedestrian crashes (n = 103) head and neck injuries were in general due to hitting the windscreen frame, while in vehicle-to-bicycle crashes (n = 100) head and neck injuries were typically sustained by ground impact. Abdominal, pelvic and thoracic injuries in pedestrians and thoracic injuries in bicyclists were in general caused by impacting the bonnet. In vehicle-to-pedestrian crashes, energy reducing airbags at critical impact points with low yielding ability on the car, as the bonnet and the windscreen frame, might reduce injuries. As vehicle-to-bicyclist crashes occurred mostly in good lighting conditions and visibility and the ground impact causing almost four times as many injuries as an impact to the different regions of the car, crash avoidance systems as well as separating bicyclists from motor traffic, may contribute to mitigate these injuries.