Pricing Vulnerable Options in a Mixed Fractional Brownian Motion with Jumps

A new framework for pricing European vulnerable options is developed in the case where the underlying stock price and firm value follow the mixed fractional Brownian motion with jumps, respectively. This research uses the actuarial approach to study the pricing problem of European vulnerable options. An analytic closed-form pricing formula for vulnerable options with jumps is obtained. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the paper. Finally, we compare and analyze the pricing results of different pricing models and discuss the influences of basic parameters on the pricing results of our proposed model by using numerical simulations, and the corresponding economic analyses about these influences are given.

Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. By using the actuarial approach, analytic formulae for pricing the European vulnerable options are derived. The proposed pricing model contains many existing models such as Black–Scholes model (1973), Merton jump-diffusion model (1976), Klein model (1996), and Tian et al. model (2014).

Betting Against the Odds: The Mysterious Case of the Clinical Override in Risk Assessment of Adult Convicted Offenders

Various tools were designed to guide practitioners in the risk assessment of offenders, including the Level of Service and Case Management Inventory (LS/CMI). This instrument is based on risk assessment principles prioritizing the actuarial approach to clinical judgment. However, the tool’s architects allowed subjective judgment from the practitioners—referred to as clinical override—to modify an offender’s risk category under certain circumstances. Few studies, however, have examined these circumstances. Therefore, the current study used decision tree analyses among a quasi-population of Quebec offenders ( n = 15,744) to identify whether there are offenders more likely to be subjected to this discretion based on their characteristics. The results suggest that, although the override is rare, it occurred under few specific combinations of circumstances. More precisely, these findings propose that the utilization of the clinical override stems from a perceived discrepancy between risk prediction and management.

Mining Actuarial Risk Predictors in Accident Descriptions Using Recurrent Neural Networks

One crucial task of actuaries is to structure data so that observed events are explained by their inherent risk factors. They are proficient at generalizing important elements to obtain useful forecasts. Although this expertise is beneficial when paired with conventional statistical models, it becomes limited when faced with massive unstructured datasets. Moreover, it does not take profit from the representation capabilities of recent machine learning algorithms. In this paper, we present an approach to automatically extract textual features from a large corpus that departs from the traditional actuarial approach. We design a neural architecture that can be trained to predict a phenomenon using words represented as dense embeddings. We then extract features identified as important by the model to assess the relationship between the words and the phenomenon. The technique is illustrated through a case study that estimates the number of cars involved in an accident using the accident’s description as input to a Poisson regression model. We show that our technique yields models that are more performing and interpretable than some usual actuarial data mining baseline.

An Actuarial Approach for Modeling Pandemic Risk

In this article, a model for pandemic risk and two stochastic extensions is proposed. It is designed for actuarial valuation of insurance plans providing healthcare and death benefits. The core of our approach relies on a deterministic model that is an efficient alternative to the susceptible-infected-recovered (SIR) method. This model explains the evolution of the first waves of COVID-19 in Belgium, Germany, Italy and Spain. Furthermore, it is analytically tractable for fair pure premium calculation. In a first extension, we replace the time by a gamma stochastic clock. This approach randomizes the timing of the epidemic peak. A second extension consists of adding a Brownian noise and a jump process to explain the erratic evolution of the population of confirmed cases. The jump component allows for local resurgences of the epidemic.

PENDEKATAN STRATEGIS ADAPTIF BERBASIS SJSN (BPJS) DALAM UPAYA PENGEMBANGAN PRODUK PENSIUN NASIONAL

ABSTRACT The Capital Market Industry and Non-Bank Financial Institutions (NBFIs) provide alternative means of investment and financial planning for the public. Funds collected in the capital market and the non-bank financial industry (IKNB) and the movement of funds through the financial markets, including capital markets and non-bank financial institutions, are the main keys to the movement of a country's economy. The ranking of penetration results from the World Bank in 6 Asian countries Indonesia ranks 6th, in order to increase penetration, an adaptive approach based on the National Social Security System (BPJS) is needed, in this case placing the role of the National Health Insurance as a center for developing a national pension program with the strategy of integrating the health benefits of Social Security Health Insurance. and pension services (BPJS-K & P). The purpose of this research is to analyze and study innovation solutions to the development and derivation platform of pension products based on the BPJS program. This study uses a descriptive analytical research design and an actuarial approach to research and develop BPJS-based pension services programs. Keywords: Adaptive Strategy, SJSN, BPJS, Pension Services. ABSTRAK Industri Pasar Modal dan Lembaga Keuangan Non-Bank (LKNB) menyediakan sarana investasi alternatif dan perencanaan keuangan untuk publik. Dana yang dikumpulkan di pasar modal dan industri keuangan non-bank (IKNB) dan pergerakan dana melalui pasar keuangan, termasuk pasar modal dan lembaga keuangan non-bank, adalah kunci utama pergerakan ekonomi suatu negara. Pemeringkatan hasil penetrasi dari Bank Dunia di 6 negara Asia Indonesia menempati urutan keenam, untuk meningkatkan penetrasi, diperlukan pendekatan adaptif berdasarkan Sistem Jaminan Sosial Nasional (BPJS), dalam hal ini menempatkan peran Asuransi Kesehatan Nasional. sebagai pusat pengembangan program pensiun nasional dengan strategi mengintegrasikan manfaat kesehatan dari Jaminan Kesehatan Jaminan Sosial. dan layanan pensiun (BPJS-K & P). Tujuan dari penelitian ini adalah untuk menganalisis dan mempelajari solusi inovasi untuk platform pengembangan dan derivasi produk pensiun berdasarkan program BPJS. Penelitian ini menggunakan desain penelitian analitik deskriptif dan pendekatan aktuaria untuk meneliti dan mengembangkan program layanan pensiun berbasis BPJS. Kata kunci: Strategi Adaptif, SJSN, BPJS, Layanan Pensiun.

Bühlmann & Bühlmann-Straub Credibility for Extreme Claims Applied on Non-Life Egyptian Insurance Market: An Actuarial Approach

Credibility theory is an actuarial approach used to calculate the short term insurance premiums. The aim of this article is to calculate the credibility premium based on real data from non-life Egyptian insurance industry during 10 years period (2006 to 2015), taking into consideration the amount of incurred claims from six insurance branches and the number of extreme losses in each branch. The analysis was based on the assumptions of Bühlmann and Bühlmann-Straub credibility models in order to estimate the net credible premium for the upcoming year as a linear function of the prior claims and the number of extreme events.

Optimising Contribution Rate for SOCSO’s Invalidity Pension Scheme: Actuarial Present Value (APV)

This study proposes the optimization of the contribution rate for Social Security Organization (SOCSO)’s Invalidity Pension Scheme (IPS). This study aims to statistically analyses the current situation of the contribution fund collection and the claim benefits payment under SOCSO’s IPS. It seeks to develop an actuarial formulation based on the benefits coverage from SOCSO’s IPS. It attempts to determine an optimal contribution rate to support the benefits provided under SOCSO’s IPS using an actuarial approach. It proposes an appropriate contribution rate to be implemented by SOCSO. Currently, the contribution rate for SOCSO’s IPS is 1%, which is shared equally between employer and employee. This contribution rate is directly deducted from the employee’s monthly gross salary. This contribution rate needs to be adjusted upwards by SOCSO soon to ensure that all payments of claims are sufficiently covered. Based on the 9th Actuarial Valuation Report issued by the International Labour Organization (ILO), recent statistics show that immediate revision of contribution rate is necessary to achieve the minimum loss ratio (max 20%) in SOCSO’s IPS funding systems. In this study, the Actuarial Present Value Approach is applied to all benefits under SOCSO’s IPS. SOCSO data from 1985 until 2014 are used in this study. Seven assumptions are made in this study namely mortality rate, salary ceiling, interest rate, retirement age, increment salary rate, age entry, and salary entry. By optimizing the worst-case scenario (single simulation), this study has found that the optimal contribution rate is 2.2% rather than the current 1%. This can be attributed to the fact that since 1969, many changes have occurred in the workplace, working conditions are different and many new jobs have been created. Therefore, an Actuarial Present Value Approach with regards to actuarial modeling was conducted to optimize SOCSO’s IPS contribution rate. In conclusion, an optimal contribution rate of 2.2% should be introduced and implemented in the future as part of the efforts to reduce society’s burden whilst ensuring that adequate protection is provided to the nation’s workforce.

Assessing risk of opioid misuse in the treatment of chronic pain: Building a practical actuarial approach

Objective: Opioid misuse risk assessment has been highlighted as an important part of clinical practice, but there is a paucity of research identifying an effective approach to assessment. Currently, practitioners use patient history, interviews, and formal questionnaires, and these data are weighed clinically to assign risk. The authors propose the use of an actuarial method—the Bayesian nomogram—as a simple, standard, evidence-based approach to opioid misuse risk assessment.Interventions: The Bayesian nomogram relies solely on empirically established relationships between risk factors and risk and has been found in other fields to be both more efficient and more consistent than clinical judgment. The authors performed a comprehensive search of the literature to identify empirically established risk factors for opioid misuse in the treatment of noncancer chronic pain.Results: As the Bayesian nomogram requires both base rates of the predicted event (opioid misuse) and odds ratios for risk factors, the authors reported the most current evidence available in the literature. The authors also included the nomogram itself for easy clinical application of base rates and risk factors in the predictive model. Finally, the authors provided examples to help illustrate practical application.Conclusions: The authors call for research comparing this methodology to “assessment as usual” to better predict risk of opioid misuse and to aid decision making for medical providers treating chronic-pain patients.