Optimal Investment in the Development of Oil and Gas Field

Let an oil and gas field consists of clusters in each of which an investor can launch at most one project. During the implementation of a particular project, all characteristics are known, including annual production volumes, necessary investment volumes, and profit. The total amount of investments that the investor spends on developing the field during the entire planning period we know. It is required to determine which projects to implement in each cluster so that, within the total amount of investments, the profit for the entire planning period is maximum. The problem under consideration is NP-hard. However, it is solved by dynamic programming with pseudopolynomial time complexity. Nevertheless, in practice, there are additional constraints that do not allow solving the problem with acceptable accuracy at a reasonable time. Such restrictions, in particular, are annual production volumes. In this paper, we considered only the upper constraints that are dictated by the pipeline capacity. For the investment optimization problem with such additional restrictions, we obtain qualitative results, propose an approximate algorithm, and investigate its properties. Based on the results of a numerical experiment, we conclude that the developed algorithm builds a solution close (in terms of the objective function) to the optimal one

Implementation of an epicardial implantable MEMS sensor for continuous and real-time postoperative assessment of left ventricular activity in adult minipigs over a short- and long-term period

The sensing of left ventricular (LV) activity is fundamental in the diagnosis and monitoring of cardiovascular health in high-risk patients after cardiac surgery to achieve better short- and long-term outcome. Conventional approaches rely on noninvasive measurements even if, in the latest years, invasive microelectromechanical systems (MEMS) sensors have emerged as a valuable approach for precise and continuous monitoring of cardiac activity. The main challenges in designing cardiac MEMS sensors are represented by miniaturization, biocompatibility, and long-term stability. Here, we present a MEMS piezoresistive cardiac sensor capable of continuous monitoring of LV activity over time following epicardial implantation with a pericardial patch graft in adult minipigs. In acute and chronic scenarios, the sensor was able to compute heart rate with a root mean square error lower than 2 BPM. Early after up to 1 month of implantation, the device was able to record the heart activity during the most important phases of the cardiac cycle (systole and diastole peaks). The sensor signal waveform, in addition, closely reflected the typical waveforms of pressure signal obtained via intraventricular catheters, offering a safer alternative to heart catheterization. Furthermore, histological analysis of the LV implantation site following sensor retrieval revealed no evidence of myocardial fibrosis. Our results suggest that the epicardial LV implantation of an MEMS sensor is a suitable and reliable approach for direct continuous monitoring of cardiac activity. This work envisions the use of this sensor as a cardiac sensing device in closed-loop applications for patients undergoing heart surgery

Diverse Beliefs and Time Variability of Risk Premia

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental primitive state variable. Market belief is observable; it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive equilibrium asset prices and implied risk premium. Our approach permits a closed form solution of prices; hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions. Our main result is that, above the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3- and 6-month Treasury Bills (T-Bills). The annual mean risk premium on holding such assets for 1-12 months is about 40-60 basis points and we find that, on average, the component of market belief in the risk premium exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2 months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. "bull" markets) are shown to be periods when the market risk premium is low while in periods of pessimism (i.e. "bear" markets) the market's risk premium is high. Fluctuations in risk premia are thus inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant

A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same e±ciency as Barone-Adesi and Whaley's (1987) quadratic approximation with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston's stochastic volatility model, our method is shown to be extremely e±cient and fairly accurate