O debate acerca do equilíbrio financeiro e atuarial dos regimes de previdência social é tema relevante e de alta indagação no momento atual da economia brasileira, e em particular, na gaúcha. Os diferentes regimes de previdência social adotados no Brasil e seus modelos de financiamento devem estar intimamente ligados ao equilíbrio financeiro e atuarial, adequados a soluções que permitam o atingimento de seus fins precípuos, voltados à garantia do pagamento de benefícios a seus segurados, sem que, no entanto, esse proceder gere prejuízos nas contas públicas e outros aportes estatais. No âmbito do Rio Grande do Sul, as fórmulas encontradas ao longo de décadas objetivando a solidez do regimes previdenciários aqui adotados, não discrepam daquelas adotadas em âmbito nacional e resumem-se basicamente a três pontos: sucessivas alterações legislativas com a mudança do modelo de financiamento da repartição simples para o da capitalização; a majoração paulatina das alíquotas que se constituem na principal fonte de receita do sistema; e a instituição do regime de previdência complementar. A (in)adequação de medidas adotadas no regime próprio de previdência gaúcho voltadas à busca do equilíbrio financeiro e atuarial foi a resposta encontrada ao que se propôs analisar na presente dissertação. / The debate about the financial and actuarial balance of social security regimes is an important and highly discussed subject at the current moment of the Brazilian economy, and particularly in Rio Grande do Sul. The different types of social security systems adopted in Brazil as well as their funding models must be closely linked to the financial and actuarial balance, being appropriate to solutions that enable the achievement of their main purposes, aimed at ensuring the payment of benefits to its policyholders, however, in a manner that this proceeding doesn’t generate any losses in the public accounts as well as at any other state contributions. In the scope of Rio Grande do Sul, the formulas found along decades aiming the trustworthiness of the social security schemes adopted here, do not disagree from those adopted at the national level and thus can be summarized basically into three points: successive legislative alterations with the changing of the funding model from the simple sharing model to the capitalization one; the gradual increase in rates that are the main source of system revenues; and the institution of the complementary pension regime. The (in) adequacy of measures taken in the Rio Grande do Sul own Special Security Regime that aimed the pursuit of financial and actuarial balance was found as the answer for what this dissertation proposed to analyse.

聯合國以老年人口佔總人口數百分之七作為老人國分類標準的比率,依據我國六十五歲老年人口截至民國八十二年九月底已佔總人口7,02%,顯示我國已正式邁入高齡化國家。政府為了解決高齡化社會所將帶來的老人生理方面和經濟方面的問題,已於民國八十四年三月一日起,實施全民健康,保險制度,以提供老年人部份的醫療需求;並擬規劃開辦國民年金保險,以提供老年人基本經濟生活之保障。國民年金保險為一種長期性的社會保險,故制度是否能健全,就緊檕於整體性的長期財務規劃是否完備。綜觀目前已實施國民年金保險制度的先進國家,大多因先其前財務規劃未盡健全,以致年金財務會發生危機,也造成了政府財政上的負擔。因此在國民年金險制度研擬規劃之初,本文欲藉著模擬分析方法加以研究,以提供可行之財務制度及制度財務狀況。

<p>Standarden IAS 19, ersättningar till antällda, infördes den 1 januari 2005. Standarden behandlar fyra olika områden, ett av dem är ersättning efter avslutad anställning i form av pensioner. En förmånsbestämd pensionsplan innebär att en anställd vid pensionsavgång får en garanterad förmån. För att företaget på ett tillförlitligt sätt ska redovisa denna framtida skuld, måste de uppskatta ett antal olika aktuariella antaganden. Svårigheterna med dessa uppskattningar och vårt intresse för pensionsredovisning, mynnade ut i denna uppsats problemformulering: Hur sker och uppfattas arbetet med de aktuariella antagandena? Syftet är att genom en enkätstudie med företag på Stockholmsbörsen och telefonintervjuer med aktuarier kartlägga hur arbetet med de aktuariella antagandena ser ut och även skapa oss en uppfattning om hur respondenterna bedömer den nya standarden jämfört med tidigare praxis och norm.</p><p>Vi vill tolka och försöka förstå hur arbetet kan se ut hos de personer som arbetar med de aktuariella antagandena. I enlighet med den hermeneutiska kunskapssynen anser vi att kunskap om detta, inte uppnås genom mätning utan genom att tolka och förstå företagen och aktuariernas utsagor.Därför lämpar sig det hermeneutiska synsättet bäst. Den teoretiska referensramen utgörs av dels en bakgrund till IAS/IFRS och det svenska pensionssystemet och dels av en utförligare beskrivning av redovisningen av de förmånsbestämda pensionsplanerna, där de aktuariella antagandena utgör en viktig del. Eftersom vi ansåg att den tidigare forskningen som fanns var användbar, valde vi ett deduktivt angreppssätt för att ta oss an studiens problem. Studien består som tidigare nämnt av både en kvantitativ undersökning i form av en enkät och en kvalitativ undersökning i form av telefonintervjuer. Anledningen till detta var att vi ville belysa samarbetet mellan aktuarier och företag och på så sätt få en djupare förståelse för ämnet.</p><p>Resultatet av studien visar att aktuarierna fått en mer betydande roll efter införandet av IAS 19, även om många företag uppskattar sina antaganden själva. Personalomsättning ansågs huvudsakligen vara svårast att uppskatta, medan diskonteringsräntan ansågs ha mest effekt på pensionsskulden. Företagen omprövade sina antaganden antingen med ett års eller ett kvartalsvis intervall. Den vanligaste redovisningsmetoden för de aktuariella vinsterna och förlusterna var korriodorregeln. Det var främst de större företagen som hade börjat gå över till den alternativa metoden, direkt mot eget kapital. Den nya standarden ansågs vara mer tillförlitlig och ge en mer enhetlig redovisning. Övergången till den nya standarden hade dock inneburit mycket merarbete och höga kostnader.</p>

Standarden IAS 19, ersättningar till antällda, infördes den 1 januari 2005. Standarden behandlar fyra olika områden, ett av dem är ersättning efter avslutad anställning i form av pensioner. En förmånsbestämd pensionsplan innebär att en anställd vid pensionsavgång får en garanterad förmån. För att företaget på ett tillförlitligt sätt ska redovisa denna framtida skuld, måste de uppskatta ett antal olika aktuariella antaganden. Svårigheterna med dessa uppskattningar och vårt intresse för pensionsredovisning, mynnade ut i denna uppsats problemformulering: Hur sker och uppfattas arbetet med de aktuariella antagandena? Syftet är att genom en enkätstudie med företag på Stockholmsbörsen och telefonintervjuer med aktuarier kartlägga hur arbetet med de aktuariella antagandena ser ut och även skapa oss en uppfattning om hur respondenterna bedömer den nya standarden jämfört med tidigare praxis och norm. Vi vill tolka och försöka förstå hur arbetet kan se ut hos de personer som arbetar med de aktuariella antagandena. I enlighet med den hermeneutiska kunskapssynen anser vi att kunskap om detta, inte uppnås genom mätning utan genom att tolka och förstå företagen och aktuariernas utsagor.Därför lämpar sig det hermeneutiska synsättet bäst. Den teoretiska referensramen utgörs av dels en bakgrund till IAS/IFRS och det svenska pensionssystemet och dels av en utförligare beskrivning av redovisningen av de förmånsbestämda pensionsplanerna, där de aktuariella antagandena utgör en viktig del. Eftersom vi ansåg att den tidigare forskningen som fanns var användbar, valde vi ett deduktivt angreppssätt för att ta oss an studiens problem. Studien består som tidigare nämnt av både en kvantitativ undersökning i form av en enkät och en kvalitativ undersökning i form av telefonintervjuer. Anledningen till detta var att vi ville belysa samarbetet mellan aktuarier och företag och på så sätt få en djupare förståelse för ämnet. Resultatet av studien visar att aktuarierna fått en mer betydande roll efter införandet av IAS 19, även om många företag uppskattar sina antaganden själva. Personalomsättning ansågs huvudsakligen vara svårast att uppskatta, medan diskonteringsräntan ansågs ha mest effekt på pensionsskulden. Företagen omprövade sina antaganden antingen med ett års eller ett kvartalsvis intervall. Den vanligaste redovisningsmetoden för de aktuariella vinsterna och förlusterna var korriodorregeln. Det var främst de större företagen som hade börjat gå över till den alternativa metoden, direkt mot eget kapital. Den nya standarden ansågs vara mer tillförlitlig och ge en mer enhetlig redovisning. Övergången till den nya standarden hade dock inneburit mycket merarbete och höga kostnader.

Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

Main focus is to extend the analysis of the ruin related quantities, such as the surplus immediately prior to ruin, the deficit at ruin or the ruin probability, to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and two important equations that are used as frameworks are derived. These equations are extended from the ordinary renewal risk model to the delayed renewal risk model. The first equation is obtained by conditioning on the first drop below the initial surplus level, and the second equation by conditioning on the amount and the time of the first claim. Then, we consider the deficit at ruin in particular among many random variables associated with ruin and six main results are derived. We also explore how the Gerber-Shiu expected discounted penalty function can be expressed in closed form when distributional assumptions are given for claim sizes or the time until the first claim. Lastly, we consider a model that has premium rate reduced when the surplus level is above a certain threshold value until it falls below the threshold value. The amount of the reduction in the premium rate can also be viewed as a dividend rate paid out from the original premium rate when the surplus level is above some threshold value. The constant barrier model is considered as a special case where the premium rate is reduced to $0$ when the surplus level reaches a certain threshold value. The dividend amount paid out during the life of the surplus process until ruin, discounted to the beginning of the process, is also considered.

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

The subject of the study for this dissertation is the relationship between pricing and reserving risks for property-casualty insurance companies. Since the risk characteristics of insurers differ based on their structure, objectives and incentives, segmenting the insurers into subgroups would allow for a better understanding of group-specific risks. Based on this approach to analyzing insurer financial risks, we find that, in a given accident year, the pricing and reserving errors are positively correlated, especially in long-tailed lines of business. Large insurers, stock insurers, and multi-state insurers, in general, exhibit a strong correlation between accident-year price and reserve errors. However, only size of insurers appears to be a factor that influences the interaction between price changes and the calendar year loss reserve adjustments. Furthermore, we find that the pricing risk and reserving risk are marginally more homogenous within a market segment when size, type and number of states are employed as criteria for market segmentation, hence insurance regulators should consider the refined market segments for the RBC formula. The empirical results also indicate that, in general, Chain-Ladder reserving method likely contributes to loss reserve errors when there is a change in the loss development pattern and the magnitude of the errors is worse for large insurers. Finally, we find that our proposed measurement method for the product diversification benefit provides support for the notion that the diversification benefit on the incurred losses increases with the number of lines in the portfolio. Yet, the diminishing returns tend to decrease the diversification benefit on the incurred losses for insurers that write the business in more than six of the selected lines. To the contrary, our proposed measure does not provide clear evidence that writing business in many product lines increases the product diversification benefit with respect to adverse loss development. We do find that the diversification benefit for both incurred losses and loss development is higher for larger insurers. Hence, for risk management and regulatory purposes, a stronger case can be made for considering firm size than product diversification.

Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by \[ \max_{k=0, \ldots, t} S_k - S_t, \] where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time.

Main focus is to extend the analysis of the ruin related quantities, such as the surplus immediately prior to ruin, the deficit at ruin or the ruin probability, to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and two important equations that are used as frameworks are derived. These equations are extended from the ordinary renewal risk model to the delayed renewal risk model. The first equation is obtained by conditioning on the first drop below the initial surplus level, and the second equation by conditioning on the amount and the time of the first claim. Then, we consider the deficit at ruin in particular among many random variables associated with ruin and six main results are derived. We also explore how the Gerber-Shiu expected discounted penalty function can be expressed in closed form when distributional assumptions are given for claim sizes or the time until the first claim. Lastly, we consider a model that has premium rate reduced when the surplus level is above a certain threshold value until it falls below the threshold value. The amount of the reduction in the premium rate can also be viewed as a dividend rate paid out from the original premium rate when the surplus level is above some threshold value. The constant barrier model is considered as a special case where the premium rate is reduced to $0$ when the surplus level reaches a certain threshold value. The dividend amount paid out during the life of the surplus process until ruin, discounted to the beginning of the process, is also considered.