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This module will introduce the techniques and contemporary methods used in active remote sensing systems, focusing on LIDAR and RADAR systems. The module will cover the fundamental principles of active remote sensing (e.g. the measurement techniques of these systems). Additionally, the module will focus on practical application areas of data from these systems, specifically in terrestrial systems, such as three-dimensional (3D) topographic mapping, forests characteristics mapping and surface deformation.

This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.

The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.

This module is a pre-requisites for MATH6130

This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.

The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.

This module is a pre-requisites for MATH6130

This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.

The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.

This module is a pre-requisites for MATH6130

This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.

The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.

Pre-requisite for MATH3066

This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.

The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.

This module is a pre-requisites for MATH6130

This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.

The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.

Pre-requisite for MATH3066

Synopsis:
The module extends the mathematical framework developed in MATH3063 in order to enable modelling of long term financial transactions where the various cash flows are contingent on the death or survival of several lives, or where there are several competing sources of decrement present. Having extended this framework, we can address pricing and reserving issues for contracts on a pair of lives, such as a husband and wife.

The module begins by extending the notion of a life table to several lives, as a precursor to examining assurances on a pair of lives where the benefit is paid on the first (joint life assurance) or last (last survivor assurance) of the pair to die. Assurances payable only on a specified ordering of the deaths (contingent assurances) are also covered, as are correspondingly ordered annuities (reversionary annuities).

Attention then turns to a single life subject to several competing sources of decrement who may leave the population of active members by age retirement, by ill-health retirement, by death, or by leaving employment covered by the scheme. Both multiple-state and multiple-decrement models are employed in such contexts, and both are examined.

The concepts of aggregate claim and cash-flow process are explained. Then Poisson process are used to model the number of claims, and the distribution of inter-arrival claims are discussed. The concept of ruin probability is covered where compound poison processes and simulation techniques are covered to calculate various type of finite and infinite horizon ruin probabilities. Next, the method of chain ladder and their application in delay trainable are studied where inflation is allowed and statistical models are applied. Finally, Bornhuetter-Ferguson method for estimating outstanding claim amounts are investigated.

Synopsis:
The module extends the mathematical framework developed in MATH3063 in order to enable modelling of long term financial transactions where the various cash flows are contingent on the death or survival of several lives, or where there are several competing sources of decrement present. Having extended this framework, we can address pricing and reserving issues for contracts on a pair of lives, such as a husband and wife.

The module begins by extending the notion of a life table to several lives, as a precursor to examining assurances on a pair of lives where the benefit is paid on the first (joint life assurance) or last (last survivor assurance) of the pair to die. Assurances payable only on a specified ordering of the deaths (contingent assurances) are also covered, as are correspondingly ordered annuities (reversionary annuities).

Attention then turns to a single life subject to several competing sources of decrement who may leave the population of active members by age retirement, by ill-health retirement, by death, or by leaving employment covered by the scheme. Both multiple-state and multiple-decrement models are employed in such contexts, and both are examined.

The concepts of aggregate claim and cash-flow process are explained. Then Poisson process are used to model the number of claims, and the distribution of inter-arrival claims are discussed. The concept of ruin probability is covered where compound poison processes and simulation techniques are covered to calculate various type of finite and infinite horizon ruin probabilities. Next, the method of chain ladder and their application in delay trainable are studied where inflation is allowed and statistical models are applied. Finally, Bornhuetter-Ferguson method for estimating outstanding claim amounts are investigated.

Synopsis:
The module extends the mathematical framework developed in MATH3063 in order to enable modelling of long term financial transactions where the various cash flows are contingent on the death or survival of several lives, or where there are several competing sources of decrement present. Having extended this framework, we can address pricing and reserving issues for contracts on a pair of lives, such as a husband and wife.

The module begins by extending the notion of a life table to several lives, as a precursor to examining assurances on a pair of lives where the benefit is paid on the first (joint life assurance) or last (last survivor assurance) of the pair to die. Assurances payable only on a specified ordering of the deaths (contingent assurances) are also covered, as are correspondingly ordered annuities (reversionary annuities).

Attention then turns to a single life subject to several competing sources of decrement who may leave the population of active members by age retirement, by ill-health retirement, by death, or by leaving employment covered by the scheme. Both multiple-state and multiple-decrement models are employed in such contexts, and both are examined.

The concepts of aggregate claim and cash-flow process are explained. Then Poisson process are used to model the number of claims, and the distribution of inter-arrival claims are discussed. The concept of ruin probability is covered where compound poison processes and simulation techniques are covered to calculate various type of finite and infinite horizon ruin probabilities. Next, the method of chain ladder and their application in delay trainable are studied where inflation is allowed and statistical models are applied. Finally, Bornhuetter-Ferguson method for estimating outstanding claim amounts are investigated.