Application of Coherent Risk Measures to Capital Requirements in Insurance

Risk measurements go hand in hand with setting of capital minima by companies as well as by regulators. We review the properties of coherent risk measures and examine their implications for capital requirement in insurance. We also comment on the specific risk-based capital computations.     

Risk management lessons from Long‐Term Capital Management

The 1998 failure of Long‐Term Capital Management (LTCM) is said to have nearly blown up the world's financial system. For such a near‐catastrophic event, the finance profession has precious little information to draw from. By piecing together publicly available information, this paper draws risk management lessons from LTCM. LTCM's strategies are analysed in terms of the fund's Value at Risk (VAR) and the amount of capital necessary to support its risk profile. The paper shows that LTCM had severely underestimated its risk due to its reliance on short‐term history and risk concentration. LTCM also provides a good example of risk management taken to the extreme. Using the same covariance matrix to measure risk and to optimize positions inevitably leads to biases in the measurement of risk. This approach also induces the strategy to take positions that appear to generate 'arbitrage' profits based on recent history but also represent bets on extreme events, like selling options. Overall, LTCM's strategy exploited the intrinsic weaknesses of its risk management system.     

Dynamic duopoly with learning through market experimentation

Summary This paper analyzes how learning behaviors can substantially modify the outcome of competition in an oligopolistic industry facing demand uncertainty. We consider the case of a symmetric duopoly game where firms have imperfect information about market demand and learn through observing the volume of their sales. The main body of the paper consists in showing how market experimentation can explain the existence ofprice-dispersion in an oligopolistic industry. We study this phenomenon and its dynamic evolution in the context of an Hotelling duopoly model; we then extend the analysis to general demand functions and toN-firm oligopolies. We discuss some implications of the public good aspect of information about market demand. We then conclude with a few comments on what happens when the value of information in the oligopolistic industry is negative.We are very grateful to Patrick Bolton for his helpful advice. We also wish to thank Richard Caves, Anthony Creane, Jean-Jacques Laffont, Andreu Mas-Colell, Eric Maskin, Jean-Charles Rochet, Margaret Slade, John Sutton, Jean Tirole, Mike Whinston and an anonymous referee.     

Construction of a state space for interrelated securities with an application to temporary equilibrium theory

Summary We construct an endogenous state space in an exchange economy with possibly infinite horizon. Every period agents trade securities whose payoffs depend on future dividends and asset prices. We reject the perfect foresight assumption on the ground that agents have not only limited knowledge of other individuals' endowments and preferences, but also limited capacity to compute equilibria. We choose instead absence of arbitrage as the principle which allows agents to determine if a system of future prices is possible. We give an alogrithm to compute the set of nonarbitrage prices every period, with both finite and infinite horizon. We then apply this endogenous structure of uncertainty to an infinite horizon temporary equilibrium model.I would like to thank Professor Donald Brown for his constant help and guidance. I have also greatly benefited from helpful discussions with Professors Jacques Drèze, Bernard Dumas, Mordecai Kurz, Carsten Nielsen, Jan Werner, and Ho-Mou Wu.     

Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies

Thepurpose of this short article is to simplify goodness-of-fitmethods to obtain qualitative information about returns to scalefor individual observations. Traditional and new goodness-of-fitmethods developed for estimating returns to scale on nonparametricdeterministic reference technologies are reviewed. Using compositionrules for technologies with specific returns to scale assumptions,we show how these goodness-of-fit methods can be simplified inthe case of convex technologies (Data Envelopment Analysis (DEA)models).     

Adherence,persistence, and inpatient utilization among adult schizophrenia patients using once-monthly versus twice-monthly long-acting atypical antipsychotics

Aims: This study compared healthcare resource utilization (HRU), healthcare costs, adherence, and persistence among adult patients with schizophrenia using once-monthly (OM) vs twice-monthly (TM) atypical long-acting injectable (LAI) antipsychotic (AP) therapy.

Materials and methods: A longitudinal retrospective cohort study was conducted using Medicaid claims data from six states. Patients initiated on aripiprazole or paliperidone palmitate were assigned to the OM cohort; risperidone-treated patients were assigned to the TM cohort. HRU and healthcare costs were assessed during the first 12 months following stabilization on the medication. Adherence was measured using the proportion of days covered (PDC) during the first year of follow-up. Persistence to the index medication was measured during the first 2 years following the index date. Comparison between the cohorts was achieved using multivariable generalized linear models, adjusting for demographic and clinical characteristics.

Results: Patients in the OM LAI cohort had lower inpatient HRU and medical costs when compared with patients in the TM cohort. Higher medical costs in the TM LAI cohort offset the higher pharmacy costs in the OM LAI cohort. Mean PDC during the first 12 months of follow-up was higher in the OM cohort than in the TM cohort (0.56 vs 0.50, p?<?.01). Median persistence was longer in the OM cohort than in the TM cohort (7.5 months vs 5.5 months), as was the hazard of discontinuing the index medication (hazard ratio?=?0.83, p?=?.01). Kaplan-Meier rates of persistence at 1 year were higher for OM patients than for TM patients (37.6% vs 29.6%, p?<?.01).

Limitations: This was a Medicaid sample with few aripiprazole LAI patients (5.4% of OM cohort). Medication use was inferred from pharmacy claims.

Conclusions: Among Medicaid patients in these six states, OM AP treatment was associated with lower HRU, better adherence and persistence, and similar total costs compared to patients on TM treatment.     

Healthcare resource utilization with ixazomib or placebo plus lenalidomide-dexamethasone in the randomized,double-blind,phase 3 TOURMALINE-MM1 study in relapsed/refractory multiple myeloma

Aims: The aim of this analysis was to assess healthcare resource utilization in the pivotal phase 3 TOURMALINE-MM1 study of the oral proteasome inhibitor ixazomib or placebo plus lenalidomide and dexamethasone (Rd) in relapsed and/or refractory multiple myeloma (RRMM).

Methods: In this double-blind, placebo-controlled, randomized study (NCT01564537), 722 patients with RRMM following 1–3 prior lines of therapy received Rd plus ixazomib (ixazomib-Rd; n?=?360) or matching placebo (placebo-Rd; n?=?362) until disease progression or unacceptable toxicity. Healthcare resource utilization data were captured on Day 1 of each 28-day cycle, every 4 weeks during follow-up for progression-free survival, and every 12 weeks during subsequent follow-up, and included medical encounters (length of stay, inpatient, outpatient, and reason) and number of missing days from work or other activities for patients and caregivers.

Results: Exposure-adjusted rates of hospitalization were similar between the ixazomib-Rd and placebo-Rd arms, at 0.530 and 0.564 per patient year (ppy), respectively, as were outpatient visit rates (3.305 and 3.355 ppy). Mean length of hospitalization per patient was 10.0 and 10.8 days, respectively. In both arms, hospitalization and outpatient visit rates were higher in patients with two or three prior lines of treatment (ixazomib-Rd: 0.632 and 3.909 ppy; placebo-Rd: 0.774 and 3.539 ppy) compared with patients with one prior line (ixazomib-Rd: 0.460 and 2.888 ppy; placebo-Rd: 0.436 and 3.243 ppy). Patients and their caregivers who missed any work or other activity missed a median of 7 and 5 days in the ixazomib-Rd arm, respectively, vs 8 and 4 days with placebo-Rd.

Limitations: The study was not powered for a statistical comparison of healthcare resource utilization between treatment arms, nor did it capture costs associated with utilization of the identified healthcare resources.

Conclusions: This pre-specified analysis demonstrated that the all-oral triplet regimen of ixazomib added to Rd did not increase healthcare resource utilization compared with placebo-Rd.     

Menger, Jevons, and Walras Un-homogenized, De-homogenized, and Homogenized: A Comment on Peart

Abstract . Response to Sandra J, Peart, “Jevons and Menger Re-homogenized?: Jaffé After 20 Years,” 1998. The American Journal of Economics and Sociology 57(July): 307-325.