A Delayed Black and Scholes Formula I

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent martingale measure

Canagliflozin and Cardiovascular and Renal Outcomes in Type 2 Diabetes Mellitus and Chronic Kidney Disease in Primary and Secondary Cardiovascular Prevention Groups

Background: Canagliflozin reduces the risk of kidney failure in patients with type 2 diabetes mellitus and chronic kidney disease, but effects on specific cardiovascular outcomes are uncertain, as are effects in people without previous cardiovascular disease (primary prevention). Methods: In CREDENCE (Canagliflozin and Renal Events in Diabetes With Established Nephropathy Clinical Evaluation), 4401 participants with type 2 diabetes mellitus and chronic kidney disease were randomly assigned to canagliflozin or placebo on a background of optimized standard of care. Results: Primary prevention participants (n=2181, 49.6%) were younger (61 versus 65 years), were more often female (37% versus 31%), and had shorter duration of diabetes mellitus (15 years versus 16 years) compared with secondary prevention participants (n=2220, 50.4%). Canagliflozin reduced the risk of major cardiovascular events overall (hazard ratio [HR], 0.80 [95% CI, 0.67-0.95]; P=0.01), with consistent reductions in both the primary (HR, 0.68 [95% CI, 0.49-0.94]) and secondary (HR, 0.85 [95% CI, 0.69-1.06]) prevention groups (P for interaction=0.25). Effects were also similar for the components of the composite including cardiovascular death (HR, 0.78 [95% CI, 0.61-1.00]), nonfatal myocardial infarction (HR, 0.81 [95% CI, 0.59-1.10]), and nonfatal stroke (HR, 0.80 [95% CI, 0.56-1.15]). The risk of the primary composite renal outcome and the composite of cardiovascular death or hospitalization for heart failure were also consistently reduced in both the primary and secondary prevention groups (P for interaction >0.5 for each outcome). Conclusions: Canagliflozin significantly reduced major cardiovascular events and kidney failure in patients with type 2 diabetes mellitus and chronic kidney disease, including in participants who did not have previous cardiovascular disease

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to <90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], >300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Stochastic control for linear systems driven by fractional noises

This paper is concerned with optimal control of stochastic linear systems involving fractional Brownian motion (FBM). First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. Then, three control models are formulated and studied. In the first two models, the state is scalar-valued and the control is taken as Markovian. Either the problems are completely solved based on a Riccati equation (for model 1, where the cost is a quadratic functional on state and control variables) or optimality is characterized (for model 2, where the cost is a power functional). The last control model under investigation is a general one, where the system involves the Stratonovich integral with respect to FBM, the state is multidimensional, and the admissible controls are not limited to being Markovian. A new Riccati-type equation, which is a backward stochastic differential equation involving both FBM and normal Brownian motion, is introduced. Optimal control and optimal value of the model are explicitly obtained based on the solution to this Riccati-type equation. © 2005 Society for Industrial and Applied Mathematics

A Model of Fair Process and Its Limits

Fair process research has shown that people care not only about outcomes, but also about the process that produces these outcomes. For a decision process to be seen as fair, the people affected must have the opportunity to give input and possibly to influence the decision, and the decision process and rationale must be transparent and clear. Existing research has shown empirically that fair process enhances both employee motivation and performance in execution. However, work to date has not addressed why fair process is so often violated in practice. This paper breaks new ground by analytically examining the subtle trade-offs involved. We develop a model of fair process in a principal-agent (i.e., manager-employee) context, rooted in psychological preferences for autonomy and fairness. We show that indeed fair process will not always be used, and why the hoped-for benefits may be insufficient to convince management to use fair process.fair process, engagement, transparency, social preference, agency theory, motivation