Optimal investment and risk control for an insurer under inside information

Peng, Xingchun; Wang, Wenyuan

doi:10.1016/j.insmatheco.2016.04.008

Cited by 23 publications

(10 citation statements)

References 24 publications

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“…In our framework, we interpret L as the amount of liabilities the insurer decides to take in the insurance business, and p as the premium rate the insurer receives from underwriting the policies against the risk R. This modeling choice follows from Stein (2012)[Chapter 6] and its subsequent studies such as Zou and Cadenillas (2014), Peng and Wang (2016), and Bo and Wang (2017), where the motivation comes from the AIG case in the financial crisis of 2007-2008 and argues for a negative correlation ρ < 0.…”

Section: The Market Modelmentioning

confidence: 99%

“…Such a modeling framework is general in the sense that it covers risk process models used in related literature as special cases; see, e.g., Browne (1995) and Højgaard and Taksar (1998) for early works without jumps and Zeng et al (2013) and Zeng et al (2016) for more recent works with jumps. The setup of the combined market in this paper mainly follows from that in Zou and Cadenillas (2014); see further motivations in Stein (2012) [Chapter 6] and recent papers Peng and Wang (2016) and Bo and Wang (2017). We assume the insurer can directly control her liability exposure, or alternatively, the insurer can decide the total amount of liabilities, measured by units (or the number of policies) L times R. One can easily see that such an assumption is equivalent to allowing the insurer to purchase proportional reinsurance to manage her risk exposure from underwriting.…”

Section: Introductionmentioning

confidence: 99%

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Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process

Shen

Zou

2021

Preprint

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We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem related to the original MV problem, and obtain the optimal strategy and the value function to the new problem in closed-form. We compare our formulation and optimal strategy to those under the precommitment and game-theoretic framework. Numerical studies show that, when the financial market is negatively correlated with the risk process, optimal investment may involve short selling the risky asset and, if that happens, a less risk averse insurer short sells more risky asset.

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Section: The Market Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process

Shen

Zou

2021

Preprint

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“…These problems are usual in applications of risk analysis such as portfolio choice (Zhao and Xiao, 2016), optimal reinsurance (Centeno and Simoes, 2009), combinations of both optimal investment and optimal reinsurance (Peng and Wang, 2016), etc. Moreover, as will be seen, probabilistic constraints are a particular case of V aR linked constraints.…”

Section: Optimization With Var-constraints and Probabilistic Constraintsmentioning

confidence: 99%

Differential equations connecting VaR and CVaR

Balbás

2017

Journal of Computational and Applied Mathematics

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“…Since Borch () and Arrow () proved that under adequate assumptions, the stop‐loss contract minimizes the standard deviation of the ceding company final wealth, this problem has been time and again revisited by many authors. The most recent approaches deal with general risk measures rather than the standard deviation (see, among many others, Zhuang et al., ; Weng and Zhuang, ), and sometimes also incorporate the effect of the financial market (e.g., Guan and Liang, ; Peng and Wang, ). Let us point out how the incorporation of the financial market effect may lead to nonwell‐posed optimization problems.…”

Section: Some Actuarial and Financial Implicationsmentioning

confidence: 99%

Good deal indices in asset pricing: actuarial and financial implications

Balbás

Garrido

Okhrati

2017

Int Trans Operational Res

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We integrate into a single optimization problem a risk measure, beyond the variance, and either arbitrage-free real market quotations or financial pricing rules generated by an arbitrage-free stochastic pricing model. A sequence of investment strategies such that the couple (expected return, risk) diverges to (+∞, −∞) will be called a good deal (GD). The existence of such a sequence is equivalent to the existence of an alternative sequence of strategies such that the couple (risk, price) diverges to (−∞, −∞). Moreover, by appropriately adding the riskless asset, every GD may generate a new one only composed of strategies priced at one. We will see that GDs often exist in practice, and the main objective of this paper will be to measure the GD size. The provided GD indices will equal an optimal ratio between both risk and price, and there will exist alternative interpretations of these indices. They also provide the minimum relative (per dollar) price modification that prevents the existence of GDs. Moreover, they will be a crucial instrument to detect those securities or marketed claims that are over-or underpriced. Many classical actuarial and financial optimization problems may generate wrong solutions if the used market quotations or stochastic pricing models do not prevent the existence of GDs. This fact is illustrated in the paper, and we point out how the provided GD indices may be useful to overcome this caveat. Numerical experiments are also included. Keywords: risk measure; compatibility between prices and risks; good deal size measurement; actuarial and financial implications A. Balbás et al. / Intl. Trans. in Op. Res. 26 (2019) are combined in a single problem, one often faces the existence of sequences of investment strategies (good deals or GDs) whose pairs (expected return, risk) diverge to (+∞, −∞). The existence of GDs is equivalent to the existence of alternative sequences of investment strategies whose pairs (risk, price) diverge to (−∞, −∞). This pathological finding has been analyzed in Balbás and Balbás (2009) and Balbás et al. (2016a), where explicit examples of the sequences above have been constructed and their performance empirically tested. The main conclusion was that the divergence of (expected return, risk) to (+∞, −∞) is more theoretical than real, but the performance of the constructed GD was good enough. The GD were collections of options providing much better realized Sharpe ratios than their underlying assets.In this paper, we will deal with a couple (ρ, ) composed of the risk measure ρ and the pricing rule . The pair (ρ, ) will be called noncompatible if it implies the existence of a GD, and the main objective of this paper will be the measurement of the GD size by means of a new index denoted byÑ orÑ(ρ, ). An important precedent in financial theory is the notion of arbitrage. Although the absence of arbitrage always holds in theoretical approaches, real market quotations sometimes reflect the existence of arbitrage. For this reason, some years ago many authors defined severa...

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Optimal investment and risk control for an insurer under inside information

Cited by 23 publications

References 24 publications

Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process

Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process

Differential equations connecting VaR and CVaR

Good deal indices in asset pricing: actuarial and financial implications

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