This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

Biosensors have shown great potential in realizing rapid, low cost and portable on-site detection for diseases. This work reports the development of a new bioelectronic sensor called AC electrokinetics-based capacitive (ABC) biosensor, for the detection of genomic DNA (gDNA) of methicillin-resistant Staphylococcus aureus (MRSA). The ABC sensor is based on interdigitated microelectrodes biofunctionalized with oligonucleotide probes. It uses a special AC signal for direct capacitive monitoring of topological change on nanostructured sensor surface, which simultaneously induce dieletrophoretic enrichment of target gDNAs. As a result, rapid and specific detection of gDNA/probe hybridization can be realized with high sensitivity. It requires no signal amplification such as labelling, hybridization chain reaction, or nucleic acid sequence-based amplification. This method involves only simple sample preparation. After optimization of nano-structured sensor surface and signal processing, the ABC sensor demonstrated fast turnaround of results (~10 s detection), excellent sensitivity (a detection limit of 4.7 DNA copies /µL MRSA gDNA) and high specificity, suitable for point of care diagnosis. As a bioelectronic sensor, the developed ABC sensors can be easily adapted for detection of other infectious agents.