The paper provides a representation for dynamic risk measures and capital allocations.
problem Representation of dynamic risk measures and capital allocations under Itô-Lévy model.
method Representation theorem for dynamic capital allocation derived from BSDEs with quadratic-exponential growth.
result Derivation of a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.
New risk-sharing rules induced by capital allocation principles.
problem Risk sharing in corporate structures.
method Randomizing existing capital allocation principles.
result Derives new risk-sharing rules complementing existing literature.
Study on risk sharing in capital requirements for diverse security markets.
problem Risk sharing for capital adequacy tests in heterogeneous security markets.
method Analyzes conditions for a representative agent, studies polyhedral and distribution-based constraints, proves existence of optimal allocations and equilibria.
result Existence of optimal risk allocations and equilibria under different capital adequacy constraints.
Study systemic risk measures and capital allocation rules, showing commonalities.
problem Systemic risk measures and capital allocation in financial systems.
method Developed a general framework to embed axiomatic and injective capital approaches, introduced Aumann-Shapley CAR.
result Aumann-Shapley CAR provides a universal method for capital allocation regardless of risk measurement.
New method allocates capital based on tail central moments for financial risk assessment.
problem Inability of CTE-based capital allocation to reflect tail behavior of losses.
method Developed TCM-based capital allocation for normal mean-variance mixture distributions.
result TCM-based method captures tail risk contributions not detected by CTE.
This letter assesses model risk in credit capital requirements and finds substantial tail risk.
problem Uncertainty in the probability of default and loss-given-default parameters in credit capital requirements.
method Models estimation risk in a simple way, analyzing two datasets and testing parameter dependency.
result Parameter dependency significantly increases tail risk in capital requirements, requiring substantial increases in regulatory capital.
The paper explores capital allocation using Euler formula with VaR and ES, revealing non-monotonicity and providing estimation methods.
problem Non-monotonicity in VaR-based capital allocation and the need for consistent risk measures.
method Use of Euler formula, Value-at-Risk (VaR), Expected shortfall (ES), simulation, and Markov chain Monte Carlo.
result Capital allocation with VaR is not monotonous, and consistent risk measures are crucial.
Paper uses a new copula to model risk aggregation and capital allocation.
problem Modeling dependence between risks for risk aggregation and capital allocation.
method Uses a generalized Archimedean copula (mixed Bernstein copula) to define dependence structure and derives closed-form risk measures.
result Closed-form expressions for tail value-at-risk and allocations are derived.
A Nash game theory approach allocates capital requirements among financial institutions.
problem Allocating systemic risk measures among financial institutions.
method Proposes a Nash allocation rule inspired by game theory.
result Provides sufficient conditions for the existence and uniqueness of Nash allocation rules.
Proposes a robust risk measure to minimize capital errors.
problem Minimizing capital determination errors due to risk overestimation and underestimation.
method Uses supremum over probability measures to minimize overestimation and underestimation costs.
result Guarantees the existence of a solution and explores properties of minimizer and minimum as risk and deviation measures.
Study shows how to better estimate credit provisions and economic capital.
problem Estimating credit provisions and economic capital accurately.
method Using supermodularity ordering properties and elliptically distributed latent factors.
result Convex risk measures of credit losses are nondecreasing w.r.t. various covariances.
Value-at-Risk is a flawed substitute for non-ruin capital, leading to misleading financial standards.
problem Misuse of Value-at-Risk as a risk measure, replacing non-ruin capital, leads to flawed financial standards.
method Mathematical analysis of risk measures and their implications on financial standards.
result Non-ruin capital is a more accurate risk measure than Value-at-Risk, necessitating its adoption over the former.
Credit risk may be warehoused by choice, or because of limited hedging possibilities. Credit risk warehousing increases capital requirements and leaves open risk. Open risk must be priced in the physical measure, rather than the risk neutral measure, and implies profits and losses. Furthermore the rate of return on cap…
The paper assesses methods for handling parameter uncertainty in risk capital calculations for normally distributed subrisks.
problem Parameter uncertainty in risk capital calculations for normally distributed subrisks.
method Develops a method to improve the approximation of confidence levels for both subrisks and overall risk.
result Proves a theoretical result leading to an appropriate integrated risk capital model considering parameter uncertainty.
In this paper, we address the aggregation of dependent stop loss reinsurance risks where the dependence among the ceding insurer(s) risks is governed by the Sarmanov distribution and each individual risk belongs to the class of Erlang mixtures. We investigate the effects of the ceding insurer(s) risk dependencies on th…
Study optimal portfolios of eligible assets for capital adequacy tests.
problem Finding minimal capital for passing a financial test.
method Existence and uniqueness of optimal portfolios, stability properties.
result Lower semicontinuity of optimal portfolios set-valued map, stability under polyhedral risk measures.
Although not a formal pricing consideration, gap risk or hedging errors are the norm of derivatives businesses. Starting with the gap risk during a margin period of risk of a repurchase agreement (repo), this article extends the Black-Scholes-Merton option pricing framework by introducing a reserve capital approach to …
Fair reinsurance premiums calculated for a perturbed risk model with capital injections.
problem Determining fair reinsurance premiums in a perturbed risk model with capital injections.
method Using a subordinator and Brownian perturbation, an explicit formula for reinsurance premiums is derived.
result An explicit formula for fair reinsurance premiums exists in a specific risk model setting.
We show that some specific market risk measures implied by current international capital regulation (the Basel Accords and the Capital Adequacy Directive of the European Union) violate the obvious requirement of convexity in some regions in the space of portfolio weights.
Paper introduces a framework for managing cyber risk with insurance and cybersecurity models.
problem Pervasive challenges in managing cyber risk, especially for capital allocation.
method Combines insurance frequency-severity models with cybersecurity cascade models for comprehensive cyber risk assessment. Facilitates informed capital allocation through a two-pillar framework.
result Demonstrates the necessity of comprehensive cost-benefit analysis for budget-constrained companies.
Paper introduces a new method for allocating capital based on risk measures from ruin theory.
problem Allocating capital to manage risk measures derived from ruin theory.
method Introduces a novel allocation method for dynamic value-at-risk (VaR) measures.
result Demonstrates desirable properties and compares with existing methods.
Study examines how EU's Value at Risk constraints affect insurance oligopolies.
problem Impact of EU's Value at Risk constraints on insurance oligopolies.
method Bertrand model with profit-maximizing companies facing Value at Risk constraints.
result Value at Risk constraints can lead to monopolistic premiums or market failure.
Paper develops a model to assess capital requirement for demographic risk using stochastic methods.
problem Quantifying capital requirement for demographic risk in life insurance contracts.
method Stochastic model extending local GAAP to Solvency II framework, proving market consistency.
result Model highlights main drivers of capital requirement evaluation, comparing to GAAP.
The paper analyzes risk measures and optimal reserve allocation strategies.
problem Risk measures and optimal reserve allocation across multiple lines of business.
method Formalizes expected maximum deficit, introduces implicitly bounded risk measures, and proposes capital allocation approaches.
result Theoretical results on static and dynamic coherence, convexity, and exact optimizations of aggregate minimum reserves.
We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the payoff of these assets is not…
Develops a statistical framework for coherent risk estimation.
problem Constructing coherent risk estimators with sound financial and statistical properties.
method Inspired by axiomatic risk measure theory, defines coherent risk estimators through robust representations linked to L-estimators. result Demonstrates that coherence of a risk measure does not necessarily carry over to its estimators and shows alternative weight structures can lead to different outcomes.
Study analyzes household capital risk and poverty trapping, deriving a new function for capital deficit distribution.
problem Analyzing the risk of household capital falling into poverty.
method Introduced a new Gerber-Shiu function to model trapping time and capital deficit distribution.
result Derived a model for capital deficit distribution at trapping using GB distributions.
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can…
Proposes a new method for determining LGD discount rates based on cost of capital.
problem Determining an appropriate discount rate for LGD estimation.
method Market-consistent pricing of defaulted loan portfolios to infer discount rates.
result Discount rates reflect both undiversifiable risk and time value of money.
In this paper we introduce a new coherent cumulative risk measure on RLp, the space of càdlàg processes having Laplace transform. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. Moreover, w…
Paper develops a new method for fair risk capital allocation.
problem Estimating fair risk capital allocation for portfolios with unknown laws.
method Develops a novel methodology based on coherent risk measures, focusing on expected shortfall.
result Explicit formulae and estimators for fair capital allocations are provided.
Solvency II's V@R method hides downside risk, study shows.
problem Solvency II's V@R method fails to capture extreme risks.
method Analyzes distortion risk measures and network portfolio allocations.
result Firms can reduce capital requirements by transferring risk within a network.
Study finds cryptoasset markets inefficient due to capital reallocation frictions.
problem Inefficiency in cryptoasset markets due to capital reallocation frictions.
method Examined investments with dominant and secondary risk factors, derived equilibrium restrictions, and tested empirically.
result Empirical results strongly reject necessary equilibrium restrictions, indicating market inefficiency.
By mid 2004, the Basel Committee on Banking Supervision (BCBS) is epected to launch its final recommendations on minimum capital requirements in the banking industry. Although there is the intention to arrive at capital charges which concur with economic intuition, the risk weight formulas proposed by the committee wil…
A new capital adequacy test is proposed based on value-at-risk.
problem Regulator's need for a capital adequacy test that doesn't depend on firms' surplus or currency.
method Proving that the only surplus-invariant, law-invariant, and conic acceptance set is the set of positions with negative value-at-risk.
result The value-at-risk test is the only possible capital adequacy test under specified conditions.
We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replicatio…
Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement framework. We introduce the notation of suitability of allocations for performance me…
Reinsurance can help life insurers maintain higher capital guarantees without losing utility.
problem Decreasing capital guarantees in life insurance products.
method Dynamic investment-reinsurance optimization problem with simultaneous Value-at-Risk and no-short-selling constraints. Introduced guarantee-equivalent utility gain for comparison.
result Optimally managed reinsurance allows insurers to offer higher capital guarantees without reducing expected utility.
The largest US banks are required by regulatory mandate to estimate the operational risk capital they must hold using an Advanced Measurement Approach (AMA) as defined by the Basel II/III Accords. Most use the Loss Distribution Approach (LDA) which defines the aggregate loss distribution as the convolution of a frequen…
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…
New risk measures for financial networks avoid external capital, reducing systemic risk.
problem Systemic risk in financial networks is underestimated by traditional methods.
method Developed set-valued, intrinsic risk measures for financial networks.
result Systemic intrinsic risk measures are more stable and avoid reliance on external capital.
Model shows how firms manage risk and capital in default-prone markets.
problem Managing risk and capital in firms facing default risk.
method Developed a model to characterize optimal dividend and capital structure policies.
result Optimal policy involves paying dividends to keep equity value below a critical threshold.
Model for operational risk using bipartite graphs and heavy-tailed distributions.
problem Capturing event type and business line structure in operational risk data.
method Statistical model based on heavy-tailed distributions and bipartite graphs.
result Reliable estimates of tail risk and capital allocations with small data sets.
Paper proposes a capital allocation formula for insurance companies compliant with Solvency II.
problem No specific capital allocation formula is provided for insurance companies using the Solvency II Standard Formula.
method Develops a closed formula for capital allocation that is coherent with Solvency II requirements.
result Demonstrates that the proposed allocation formula is consistent with the Euler's allocation principle.
The aim of this paper is to introduce a method for computing the allocated Solvency II Capital Requirement (SCR) of each Risk which the company is exposed to, taking in account for the diversification effect among different risks. The method suggested is based on the Euler principle. We show that it has very suitable p…
This paper examines if CTE risk measure aligns with profit-maximizing risk capital allocations.
problem Whether CTE risk measure aligns with profit-maximizing risk capital allocations.
method Exhaustive probabilistic model settings analysis.
result CTE risk measure may align with profit-maximizing risk capital allocations under certain conditions.
Paper introduces new risk measures for default risk and model uncertainty.
problem Model uncertainty and default risk in rating systems.
method Introduces default risk measures and discusses their properties and impacts.
result Different default risk measures and margins of conservatism affect risk-weighted assets.
The paper analyzes insurance risk with Parisian ruin and capital injection.
problem Analyzing insurance risk with Parisian ruin and capital injection.
method Using fluctuation and excursion theory of spectrally negative Levy processes.
result Distributional identities and ruin probabilities are derived.