Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion

Consider N independent stochastic processes \((X_i(t), t\in [0,T])\), \(i=1,\ldots , N\), defined by a stochastic differential equation with random effects where the drift term depends linearly on a random vector \(\Phi _i\) and the diffusion coefficient depends on another linear random effect \(\Psi _i\). For these effects, we consider a joint parametric distribution. We propose and study two approximate likelihoods for estimating the parameters of this joint distribution based on discrete observations of the processes on a fixed time interval. Consistent and \(\sqrt{N}\)-asymptotically Gaussian estimators are obtained when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated data and show good performances.     

When does economic model type become a decisive factor in health technology appraisals? Learning from the expanding treatment options for relapsing–remitting multiple sclerosis

Objectives: Specific economic model types often become de facto standard for health technology appraisal over time. Markov and discrete event simulation (DES) models were compared to investigate the impact of innovative modeling on the cost-effectiveness of disease-modifying therapies (DMTs) in relapsing–remitting multiple sclerosis (RRMS). Fingolimod was compared to dimethyl fumarate (DMF; in highly active [HA] RRMS), alemtuzumab (in HA RRMS) and natalizumab (in rapidly evolving severe RRMS). Comparator DMTs were chosen to reflect different dosing regimens.

Materials and methods: Markov and DES models used have been published previously. Inputs were aligned in all relevant respects, with differences in the modeling of event-triggered attributes, such as relapse-related retreatment, which is inherently difficult with a memoryless Markov approach. Outcomes were compared, with and without different attributes.

Results: All results used list prices. For fingolimod and DMF, incremental cost-effectiveness ratios (ICERs) were comparable (Markov: £4206/quality-adjusted life year [QALY] gained versus DES: £3910/QALY gained). Deviations were observed when long-term adverse events (AEs) were incorporated in the DES (Markov: £25,412 saved/QALY lost, versus DES: £34,209 saved/QALY lost, fingolimod versus natalizumab; higher ICERs indicate greater cost-effectiveness). For fingolimod versus alemtuzumab, when relapse-triggered retreatment was included in the DES, large cost differences were observed (difference between incremental cost is £35,410 and QALY is 0.10).

Limitations: UK payer perspective, therefore societal approach was not considered. Resource utilization and utilities for both models were not derived from the subpopulations; as the focus is on model type, input limitations that apply to both models are less relevant.

Conclusions: Whilst no model can fully represent a disease, a DES allows an opportunity to include features excluded in a Markov structure. A DES may be more suitable for modeling in RRMS for health technology assessment purposes given the complexity of some DMTs. This analysis highlights the capabilities of different model structures to model event-triggered attributes.     

Shrinking Cities,Shrinking Households,or Both?

Household size decline accounts for a substantial portion of population loss in shrinking cities, yet little research has focused on it. Much of the literature presents a simple growth/decline binary that is largely determined via population figures. In this paper, we highlight the importance and assess the impact of household size changes on population decline, and determine what types of household size declines are more acute in shrinking cities than other locales. We find that elderly households and households with school-aged children are under-represented in shrinking cities, while households with pre-school-aged children are over-represented. More tellingly, we find the biggest source of household-related loss in shrinking cities to be the growth of single-person households now living in houses that were once home to entire families. These findings puncture the binary on which much of the shrinking cities discourse is based. The population dynamics of most cities are subtler than either practitioners or critical scholars assert. We argue that plans and development strategies for shrinking cities should reflect a range of demographic changes, including outmigration and internal household restructuring.     

The new goods margin in new markets

We analyze the role of the new goods margin in the Baltic countries’ exports and imports growth during the 1995–2008 period. Using the methodology developed in Kehoe and Ruhl (2013), we define the set of least-traded goods as those that account for the lowest 10% of total exports and imports in 1995, and then trace its growth in several markets including the Baltics’ main trade partners, the European Union and Russia. We find that, on average, by 2008 least-traded goods accounted for nearly 50% of total Baltic exports to their main trade partners. Moreover, we find that increases in the share of least-traded exports coincided with the timing of the trade liberalization reforms implemented by the Baltic countries. Least-traded imports also grew at robust rates, but their growth was lower than that of exports, accounting for slightly less than a quarter of total imports, that is, about half of the exports value. Moreover, we find that the shares of least-traded imports from the EU 15 and from Russia started diverging around the time the Baltic countries joined the EU, with the EU 15 share increasing and the Russian one declining. We also find that the Baltics’ share of least-traded exports outpaced that of other economies in Central and Eastern Europe. Finally, exports of new goods from the Baltic countries suffered noticeably during the Global Financial Crisis. After the crisis ended, the restart in new goods exports growth displayed mixed patterns.     

ANFA — National Money Creation as an Existential Threat to the Currency Union?

The recent publication of the previously secret Agreement on Net Financial Assets (ANFA) directed the public’s attention to the possibility that national central banks could create money through purchases of securities on their own account. This paper provides an overview of the legal foundations for ANFA and shows the varying extent to which the member countries use these regulations. What are the interests, risks and consequences for the countries in crisis and the currency union as a whole? Is the ECB properly monitoring ANFA purchases? Could money creation via ANFA act as an explosive device for the currency union?     

Basic Income in the Finnish Context

The goal of the Finnish experiment that started this year is to try to get some evidence on how a new social policy instrument mimicking a basic income would work and what kind of behavioural consequences it would have. At this point, there are many strong arguments being made both in favour of and opposed to basic income. Unfortunately, there are not enough facts yet. The Finnish experiment hopes to change that.     

Autonomous Driving — a Challenge for the Automotive Industry

The automotive industry is one of the most important industries in Europe. This industry is responsible for 14% of total production and capital investment in the European manufacturing sector, and in Germany the share amounts to 22%. Structural change within this crucial sector is of relevance for the whole economy. Along with alternative propulsion systems such as electromobility, (semi-)autonomous vehicles are one of the big trends in the automotive industry. For established providers, the possibility of disruptive change poses a threat to existing markets, while a gradual introduction of new technologies also increases competition. Nevertheless, with their strong market position in the premium segment and especially their relevant research activities, European and especially German automotive manufacturers are well placed to successfully master the coming challenges in the automotive market.     

The role of measurability in game-theoretic probability

This paper argues that the requirement of measurability (imposed on trading strategies) is indispensable in continuous-time game-theoretic probability. The necessity of the requirement of measurability in measure theory is demonstrated by results such as the Banach–Tarski paradox and is inherited by measure-theoretic probability. The situation in game-theoretic probability turns out to be somewhat similar in that dropping the requirement of measurability allows a trader in a financial security with a non-trivial price path to become infinitely rich while risking only one monetary unit.     

Model uncertainty,recalibration, and the emergence of delta–vega hedging

We study option pricing and hedging with uncertainty about a Black–Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta–vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas and volgas of the non-traded and the liquidly traded options.     

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.