Multi-asset Spread Option Pricing and Hedging

We provide two new closed-form approximation methods for pricing spread options on a basket of risky assets: the extended Kirk approximation and the second-order boundary approximation. Numerical analysis shows that while the latter method is more accurate than the former, both methods are extremely fast and accurate. Approximations for important Greeks are also derived in closed form. Our approximation methods enable the accurate pricing of a bulk volume of spread options on a large number of assets in real time, which offers traders a potential edge in a dynamic market environment.multi-asset spread option, closed-form approximation

A maximum likelihood estimate of natural mortality for brown tiger prawn (Penaeus esculentus) in Moreton Bay (Australia)

The delay difference model was implemented to fit 21 years of brown tiger prawn (Penaeus esculentus) catch in Moreton Bay by maximum likelihood to assess the status of this stock. Monte Carlo simulations testing of the stock assessment software coded in C++ showed that the model could estimate simultaneously natural mortality in addition to catchability, recruitment and initial biomasses. Applied to logbooks data collected from 1990 to 2010, this implementation of the delay difference provided for the first time an estimate of natural mortality for brown tiger prawn in Moreton Bay, equal to $0.031 \pm 0.002$ week$^{-1}$. This estimate is approximately 30\% lower than the value of natural mortality (0.045 week$^{-1}$) used in previous stock assessments of this species

The Dichotomy Property in Stabilizability of 2×22\times2 Linear Hyperbolic Systems

This paper is devoted to discuss the stabilizability of a class of $2 \times2$ non-homogeneous hyperbolic systems. Motivated by the example in \cite[Page 197]{CB2016}, we analyze the influence of the interval length $L$ on stabilizability of the system. By spectral analysis, we prove that either the system is stabilizable for all $L>0$ or it possesses the dichotomy property: there exists a critical length $L_c>0$ such that the system is stabilizable for $L\in (0,L_c)$ but unstabilizable for $L\in [L_c,+\infty)$. In addition, for $L\in [L_c,+\infty)$, we obtain that the system can reach equilibrium state in finite time by backstepping control combined with observer. Finally, we also provide some numerical simulations to confirm our developed analytical criteria

Nonlinear dynamic characteristic of gear system with the eccentricity

In this paper, the dynamic behavior of a spur gear system was studied with external and internal dynamic incentive. The vibration differential equations for spur gear system were expressed in equivalent discrete models of mass, damping, and spring elements using the Lagrange equation considering the effect of lateral-torsional vibration coupling on the dynamics of gears, which was solved by the Newmark method. The investigation was carried out with multi-degree of freedom system for spur gear model, which took into account gravity, gear eccentricity, backlash, dynamic transmission error and external dynamic incentive. The lateral and torsional response characteristics of geared system were analyzed by changing the value of the rotational speed, backlash and eccentricity. It was shown from the research that the jump discontinuous phenomenon occurred at lower backlash value with increasing rotational speed and the frequency amplitudes also increased, and the regions of continuous frequency became winder when the rotational speed difference was greater. Moreover, complicated combination frequency components followed a rule of increasing firstly and then decreasing with the different backlash and eccentricity. The study may contribute to a further understanding of the dynamic characteristics of such a gear rotor-bearing system

Nonlinear behavior of a spur gear pair transmission system with backlash

In this paper, the nonlinear vibration characteristics of spur gear-rotor system and the interactions among of gear shaft, and bearing with backlash subjected to internal/external excitation are systematically investigated. The two-degree-of-freedom purely torsional generalized lumped parameter model of the spur gear system with meshing stiffness, backlash, transmission error and external periodic excitation is established. The Newmark method is used to solve simultaneously the differential equations for analysis the vibration response characteristics as well as the effects of rotational speed, backlash and mesh damping coefficient on the dynamic characteristics of the spur gear system. The numerical results clearly reveal that the system exhibits an increase mesh damping coefficient and a decrease backlash can reduce the degree of gear nonlinearity effect, which makes the meshing state of spur gear system change from double-sided impact, single-sided impact to no impact. In addition, the rotational speed has a significant effect upon the dynamic response of the system, which shows that designing a gear system to operate at a high rotational speed should be avoided especially when the rotational speed is close to the system’s natural frequency and half of the natural frequency. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a spur gear system and therefore serve as a useful source of reference for engineers in designing and controlling such systems

The Ci3+3 Design for Dual-Agent Combination Dose-Finding Clinical Trials

We propose a rule-based statistical design for combination dose-finding trials with two agents. The Ci3+3 design is an extension of the i3+3 design with simple decision rules comparing the observed toxicity rates and equivalence intervals that define the maximum tolerated dose combination. Ci3+3 consists of two stages to allow fast and efficient exploration of the dose-combination space. Statistical inference is restricted to a beta-binomial model for dose evaluation, and the entire design is built upon a set of fixed rules. We show via simulation studies that the Ci3+3 design exhibits similar and comparable operating characteristics to more complex designs utilizing model-based inferences. We believe that the Ci3+3 design may provide an alternative choice to help simplify the design and conduct of combination dose-finding trials in practice